.9999~ = 1. Prove me wrong

[SS4Brolly]

Let X = .99999~

X = .9999~
10X = 9.999~
-1X = -1X (.999~)
9X = 9
X = 1

See?

Those that have been on GameFAQ's Social boards often enough will recognize this topic. For those that havnt, this pops up occasionally and usually gets 200+ replies.

[Gothic Walrus]

Ack! LUE fad on CAG! BAD!!!

[bluetoast]

Heh, yeah there are multiple ways to prove it, I don't know why people disagree.

[Mr. Anderson]

Ouch....my brain hurts.

[DisturbedZen]

Wow ive never seen that.. but thats.. insane..

[lawyeron]

The math doesn't make sense to me.

How do you go from 10x=9.99999~
to -1x=-1x(.9999~)
If you divided both sides by -10 you would get
-x=-.9999~
and -x does not equal-x(.99999) . Try it on a calculator you will get .999999999999999999999999998


and 9x does not =9 if x=.999999999999

9*(.99999999999)=8.9999999999999999 which is almost one but not quite

The math appears to be wrong, but I'm no mathemetician. Did this really warrant 200 posts?

[video_gamer324]

This is what the concept of infinity is all about. SS4Brolly's equation demonstrates the answer to the question, "What is the largest number less than one?" The answer is nonexistent. Similarly, any number divided by infinity is zero, and any number added to or subtracted from infinity is infinity. Using infinity, answer the following question: Are there more real numbers or odd real numbers?

[JSweeney]

Here's some collaboration (http://mathforum.org/dr.math/faq/faq.0.9999.html)

Stated more simply, all it says is that as the sequence .9999999~ approaches infinity, it converges to one. The problem on gamefaqs is that the people don't have the math background, or the level headedness to actually listen. Since this can be formally proved mathematically, it cannot be disproved, unless you use shoddy math.

[godhatesjustyou]

Ouch....my brain hurts.

i feel you. :cry:

[video_gamer324]

The math doesn't make sense to me.

How do you go from 10x=9.99999~
to -1x=-1x(.9999~)
If you divided both sides by -10 you would get
-x=-.9999~
and -x does not equal-x(.99999) . Try it on a calculator you will get .999999999999999999999999998


and 9x does not =9 if x=.999999999999

9*(.99999999999)=8.9999999999999999 which is almost one but not quite

The math appears to be wrong, but I'm no mathemetician. Did this really warrant 200 posts?

See if this helps:

x=.999~
10x=10(.999~)=9.999~
10x-1x=9.999~-(.999~)
9x=9
x=1

[magilacudy]

I wouldn't be surprised if all those 200 posts were saying how stupid and corny this is. =P

Your math is wrong somehow, I think you just mixed yourself up (and me as well) on the notation.

EDIT: Directed at original post

EDIT again to JSweeney: I thought it looked a bit like CALC 1.

[godhatesjustyou]

The math doesn't make sense to me.

How do you go from 10x=9.99999~
to -1x=-1x(.9999~)
If you divided both sides by -10 you would get
-x=-.9999~
and -x does not equal-x(.99999) . Try it on a calculator you will get .999999999999999999999999998


and 9x does not =9 if x=.999999999999

9*(.99999999999)=8.9999999999999999 which is almost one but not quite

The math appears to be wrong, but I'm no mathemetician. Did this really warrant 200 posts?

See if this helps:

x=.999~
10x=10(.999~)=9.999~
10x-1x=9.999~-(.999~)
9x=9
x=1

now that makes sense!

..wow, that is really wierd..

[fuzzman24]

doesn't that whole thing depend on significant figures? if you do proper math with sig fig it does not equal out.

[SS4Brolly]

Yeah, its a tad difficult to do math on the computer.

There's another topic simmilar to this, which is easier to understand.

-4^2=-16

Because the -4 isnt in parenthesies (sp?), you square, then multiply by -1 (PEMDAS). Again, some people at GameFAQ's cannot understand this.

[EggViper]

The math doesn't make sense to me.

How do you go from 10x=9.99999~
to -1x=-1x(.9999~)
If you divided both sides by -10 you would get
-x=-.9999~
and -x does not equal-x(.99999) . Try it on a calculator you will get .999999999999999999999999998


and 9x does not =9 if x=.999999999999

9*(.99999999999)=8.9999999999999999 which is almost one but not quite

The math appears to be wrong, but I'm no mathemetician. Did this really warrant 200 posts?

See if this helps:

x=.999~
10x=10(.999~)=9.999~
10x-1x=9.999~-(.999~)
9x=9
x=1

ok correct me if im wrong but step 3 doesent seem plausible since if u are going to do something to one side of the equation u have to do the exact same thing on the other side, so adding a -1 and a -.9999 isn't quite the same.

[mojoman]

too bad it was stated that x=.99999~

[godhatesjustyou]

^^because in the first line, he stated that x=.999~
so that means that -1x = -.999~
and in line three, he substituted the -1x on the right side with -.999~

hope that helps

[spoo]

OLD'D If wanted to read LUE I would go to Gamefaqs</sigh>

[lawyeron]

That link explained it, I understand the logic now:

"Ultimately, though, this probably won't _really_ make sense until you
come to grips with what it means for a decimal to repeat _forever_,
instead of just for a r-e-a-l-l-y l-o-n-g t-i-m-e.

When you think of 0.999... as being 'a little below 1', it's because
in your mind, you've stopped expanding it; that is, instead of

0.999999...

you're _really_ thinking of

0.999...999

which is not the same thing. You're absolutely right that 0.999...999
is a little below 1, but 0.999999... doesn't fall short of 1 _until_
you stop expanding it. But you never stop expanding it, so it never
falls short of 1. "

[JSweeney]

Yeah, its a tad difficult to do math on the computer.

There's another topic simmilar to this, which is easier to understand.

-4^2=-16

Because the -4 isnt in parenthesies (sp?), you square, then multiply by -1 (PEMDAS). Again, some people at GameFAQ's cannot understand this.

Order of Operations:
Parenthesis
Expontents
Multiplication
Division
Addition
Subtraction

PEMDAS is actually a fairly decent mnemonic device for remembering that.

[st0neface]

I spent my entire Pre-calc class senior year doing stuff like that. I still pulled off a C in that class somehow. Anyways, I agree, it equals 1.

[zin63]

-4 power 2 = +16, and that's straightforward
i think sq. root of -16 is 4i where i = sq. rt -1 (or just -1 w/o sq rt) so 4i to power 2 would be -16?

and with that 0.999... i always took it as true since 1/3=0.333... 2/3=0.666... and so 3/3=0.999... except 3/3=1

ps are any mathematicians or otherwise very good math student here that can [dis]prove us all?

pps gamefaqs boarders are generally very annoying, so i never write there but sometimes read for chuckles

[JSweeney]

The biggest thing is that this usually makes that rounds in places where mathematical rigor isn't the greatest, and the mathematial understanding is at a low enough level that people haven't been introduced to Calculus and Convergent and Divergent series. After passing that point, explaining this and understanding this is fairly trivial.

[Puff Is Hurr]

Here's where u go wrong, let's say x equals .999, therefore 10x=9.99, if u subtract one x which equals .999, it would equal 8.91.

[Puff Is Hurr]

Or, otherwise if you are subtracting infinite 9's it owuld be one more than the orginal equation. Hence, I proved you wrong.

[C_A]

Ew, GameFAQs. Don't remind me of how much babysitting I had to do there.

[zin63]

oh yeah - -4 = (-1)4 not -1 X 4 so PEMDAS still favors it

same as how n pwr 2 is not n X n but n(n) there's no difference when it's just n pwr 2 but in an equation that does require pemdas it makes a big difference

[JSweeney]

You cannot prove it wrong. It is impossible.
IT CAN BE MATHEMATICALLY PROVEN TRUE, THUS IT IS TRUE.

As the infinite series .99999999999~ approaches infinity, it converges to 1. THERE ARE NO IF'S AND OR BUT'S ABOUT IT. IT IS TRUE, AND CAN BE PROVEN TO A MATHEMATICAL CERTAINTY.
If you don't believe me, check the link I provided.
You cannot prove this wrong, because it is mathematically impossible to do so. If you think you've found a way, you're wrong... it's only your misunderstanding of a concept that makes you think you are right.

[GameDude]

The world is flat. It's been mathamatically proven!

Well, that was the thought so many years ago. Just because something is mathmatically proven or thought so by the general scientific community, doesn't make it legit.

There are pink elephants with feathers.

Care to prove me wrong?

[JSweeney]

The world is flat. It's been mathamatically proven!

Well, that was the thought so many years ago. Just because something is mathmatically proven or thought so by the general scientific community, doesn't make it legit.

There are pink elephants with feathers.

Care to prove me wrong?

Really. If something can't be proven true by rigorous mathematical proof or strict adherence to the scientific method how can it be proven?
Those are the ONLY worthwhile ways of proving something legitimate.

[godhatesjustyou]

^^i agree. math can only be right or wrong, and if its proven right, it cannot be wrong.

[zin63]

gamedude - u dont make sense

the reason people thought the world is flat is BECAUSE they didn't know shitE about math, the people who did :idea: already believed the world was curved

there's a world of difference between theories and laws - .999... being 1 is a law, it's been proven, its difacto

to say it doesn't means you're saying we should throw out the numbers we've been using since forever, and make something new? Has a computer ever malfunctioned because 0.999... equals 1.

to the math-inept people - KNOW what you're talking about before saying this and that

btw, bets on how long this post goes on? :(

[E-Z-B]

This trick will work on any set of repeating numbers. Let's try an arbitrary example:

let
x = 0.285285285...
1000x = 1000*(0.285285285...)=285.285285285...

Now, subtract the equations from each other:

1000x - x = 285.285285... - 0.285285...
which equals
999x = 285

Sooooo...
x = 285/999

Put that into your calculator and see what you get.

[Mr. Anderson]

The pain inside my brain is at scorching right now. Please, somebody lock this before my head explodes.

[Scrubking]

The pain inside my brain is at scorching right now. Please, somebody lock this before my head explodes.

I like your sig, but it's a little too big. It's also stretched out.

[Mr. Anderson]

The pain inside my brain is at scorching right now. Please, somebody lock this before my head explodes.

I like your sig, but it's a little too big. It's also stretched out.

I'll try to see what I can do.

[mrtoki]

anyone who knows calculus and limits graphing should see that it's true, although the way the it's written here is a little confusing

[GameDude]

The world is flat. It's been mathamatically proven!

Well, that was the thought so many years ago. Just because something is mathmatically proven or thought so by the general scientific community, doesn't make it legit.

There are pink elephants with feathers.

Care to prove me wrong?

Really. If something can't be proven true by rigorous mathematical proof or strict adherence to the scientific method how can it be proven?
Those are the ONLY worthwhile ways of proving something legitimate.

Prove that you're not a figment of my imagination.

[magilacudy]

-4 power 2 = +16, and that's straightforward
i think sq. root of -16 is 4i where i = sq. rt -1 (or just -1 w/o sq rt) so 4i to power 2 would be -16?

and with that 0.999... i always took it as true since 1/3=0.333... 2/3=0.666... and so 3/3=0.999... except 3/3=1

ps are any mathematicians or otherwise very good math student here that can [dis]prove us all?



I was about to post about the -4 squared thing last night, but technically thats true. Its a nitpick, but (-4)^2 = 16, -4^2=-16 as the negative isnt in parentheses. I'm sure math majors get their skirts all ruffled when they see that.

I'm an engineering student so I'm going to say you're wrong, because the imaginary number should be called j. =P

As for the original mathemetical post, it seems solid to me after it was rewritten more clearly. I'm an average student but I think it'll take someone beyond the normal CAGer to disprove it, and even then it hasn't been disproven thus far. If you're going to infinity or at least infinite sums, expect to see some hiccups like that.

As for GameDude, you're getting into philosophy which doesn't fit right with this math stuff. The world wasn't mathemetically proven flat, and the scientific community never said there were any pink elephants... and not everything can be proven mathemetically.

If you really want to get into philosophy, try looking up Occam's Razor and applying it to the original post.

[nelsed]

try www.cheapassmathmatician.com ...

while there is a way to get .1111~ and .2222~ on a calculator...
there is no way to get it be .9999~ it only looks like it becuase of the digits dropped.

so theoretically 9/9 should be .9999~

since 1 / 9 = .1111~
and 2 / 9 = .2222~ etc...

[JSweeney]

The world is flat. It's been mathamatically proven!

Well, that was the thought so many years ago. Just because something is mathmatically proven or thought so by the general scientific community, doesn't make it legit.

There are pink elephants with feathers.

Care to prove me wrong?

Really. If something can't be proven true by rigorous mathematical proof or strict adherence to the scientific method how can it be proven?
Those are the ONLY worthwhile ways of proving something legitimate.

Prove that you're not a figment of my imagination.

To qoute Rene Descartes: 'I think therefore I am'.
Being a sentient intelligence, I assert my existence.
If I exist, then I cannot be a figment of your imagination.
I can prove my existence. Can you disprove it?

[bluetoast]

try www.cheapassmathmatician.com ...

so theoretically 9/9 should be .9999~

since 1 / 9 = .1111~
and 2 / 9 = .2222~ etc...

precisely why 9/9 = 1.

[GameDude]

The world is flat. It's been mathamatically proven!

Well, that was the thought so many years ago. Just because something is mathmatically proven or thought so by the general scientific community, doesn't make it legit.

There are pink elephants with feathers.

Care to prove me wrong?

Really. If something can't be proven true by rigorous mathematical proof or strict adherence to the scientific method how can it be proven?
Those are the ONLY worthwhile ways of proving something legitimate.

Prove that you're not a figment of my imagination.

To qoute Rene Descartes: 'I think therefore I am'.
Being a sentient intelligence, I assert my existence.
If I exist, then I cannot be a figment of your imagination.
I can prove my existence. Can you disprove it?

You may exist, and maybe not. Can you prove that I didn't just make your comments up?

In other words, it is impossible to prove or disprove anything, expect your existence or at least some type of that.

[Stoneage]

Man, this would make a great game.....are you listening, CAPCOM????

[organicow]

I think that tha point that Gamedude is trying to make is this: though current mathematics allows only for answers right and wrong, to say that this current incarnation of mathematical understanding is infallible would be presumptuous. To wit, future understandings of numbers and numerals may yield new options for considering equations of dispute, like these in question.

Now, I'm not getting on either side fo the fence here, because I completely blow at math. However, as someone with extensive studies in philosophy, politics, and sociology under his belt, I can state that the stubborness of some number-crunchers is staggering.

As for the Descartes debate, I will offer this:
Descartes' statements regarding "I think, therefore I am" refer to one conciousness's awareness of one's own being, and therefore creating an internal legitimacy; they do not refer to perceptions of one's conciousness by others. Descartes was not making these judgements reflecting the possibility that HIS conciousness could be the ONLY conciousness, and that all other 'beings' were merely his own self-creations.

Like I said, I'm not trying to fan any flames; just wanted to add my perspective to an unusually intellectual CAG forum!

[JSweeney]

I think that tha point that Gamedude is trying to make is this: though current mathematics allows only for answers right and wrong, to say that this current incarnation of mathematical understanding is infallible would be presumptuous. To wit, future understandings of numbers and numerals may yield new options for considering equations of dispute, like these in question.

While that's true, mathematical laws and reasoning are much more persuasive than " That's wrong because I think it's wrong.".
Of course, this is less likely to be proven wrong, as it is a quirk in the format of mathematics, and a misunderstanding on the part of most people how fractional sums are rendered. As this is a purely mathematical concept, it's much less likely that math is faulty as a base of reasoning for this. You're not applying mathematics to a wholy unknown subject, which you may or may not have full knowledge of. This is math applying itself upon itself. If you disregard this as a basis for the forumulation and proof of concepts, you must divorce yourself from almost all mathematics, as any non-trival mathematical concept must be proven, and the only to prove mathematical concepts is mathematically.

Now, I'm not getting on either side fo the fence here, because I completely blow at math. However, as someone with extensive studies in philosophy, politics, and sociology under his belt, I can state that the stubborness of some number-crunchers is staggering.

Math is not infallible. However, logic isn't either.

As for the Descartes debate, I will offer this:
Descartes' statements regarding "I think, therefore I am" refer to one conciousness's awareness of one's own being, and therefore creating an internal legitimacy; they do not refer to perceptions of one's conciousness by others. Descartes was not making these judgements reflecting the possibility that HIS conciousness could be the ONLY conciousness, and that all other 'beings' were merely his own self-creations.

Yes, but he didn't tell me to prove TO HIM that I existed. He only told me to prove that I existed, and wasn't a figment of his immagination. Therefore, I think Descartes statement's use is quite proper in this instance. Had he asked for me to prove TO HIM that I existed, it wouldn't be.

[JSweeney]

In other words, it is impossible to prove or disprove anything, expect your existence or at least some type of that.

Prove that. I can prove or disprove phenomena through proper application of the scientific method.
I can prove things on the basis of evidence and not belief.

[MorganWebbLover]

If I wanted to learn I'd go to school .

[GameDude]

In other words, it is impossible to prove or disprove anything, expect your existence or at least some type of that.

Prove that. I can prove or disprove phenomena through proper application of the scientific method.
I can prove things on the basis of evidence and not belief.

You are only want you know. Who's to say that you're not some person in an insane asylum? Can you disprove this? No. Everything you are and everything you interpret are predicated on your mind.

For instance, I don't know *for sure* if you exist. I cannot go into your mind and determine if your thoughts are coming from your mind or if I'm conjuring up them myself.

I *think* you exist, but I cannot prove it. The only evidence you have is what YOU think you have. There is no universal basis for anything.

[GameDude]

Yes, but he didn't tell me to prove TO HIM that I existed. He only told me to prove that I existed, and wasn't a figment of his immagination. Therefore, I think Descartes statement's use is quite proper in this instance. Had he asked for me to prove TO HIM that I existed, it wouldn't be.

Prove to ANYONE that you exist, besides yourself, of course. It can't be done. It can be done in your mind - and nothing else. One man's reality may not be another's. But which reality is right?

Are the "crazy" people insane or is it the non"crazy" people who are insane.

Of course, none of this really matters much. What's in my mind is all that matters - to me anyway - and that's all I really know.

[GameDude]

In other words, it is impossible to prove or disprove anything, expect your existence or at least some type of that.

Prove that. I can prove or disprove phenomena through proper application of the scientific method.
I can prove things on the basis of evidence and not belief.


I mix up "except" and "expect" up a lot. I'm an idiot.

[Persain]

i hated these topics on gamefaqs, but since there is less people here i will put in my two sence

first

9/9=1
8/9=sum 8 /10^n from n=1 to n= infinity. there is no way to express 8/9 in decimal form.
and so on down to 1/9

second

0.9999... is an asymptote to one, which means it will become infinitally close but never approach 1. ie the summation mentionated earlity is bounded by 1 but that summation is contained in a open set from zero to 1, and has no reall number which can make zero to x an closed set for x in real #'s


third

x=.999~
10x=10(.999~)=9.999~
10x-1x=9.999~-(.999~)
9x=9
x=1

this is not correct because x is a summation(not a decimal). the alebra for summations is different. if you think about it, when you multiply by 10, you add a zero to the last turm and move the decimal place over by one. but how can you add a zero to an infinite series of 9's it would imply that there is an end to the 9's which we know there isnt.

i know people will argue with me, but .999... is only considered one for ease of use, actually the limit of the series that makes up .999.. is one.

anyone else going for their phd in math here?

[JSweeney]

Prove to ANYONE that you exist, besides yourself, of course. It can't be done. It can be done in your mind - and nothing else. One man's reality may not be another's. But which reality is right?

Does it really matter? It's a fairly worthless mental exercise, at it provides no useful knowledge for application. Knowledge for it's own sake is fairly worthless.

Are the "crazy" people insane or is it the non"crazy" people who are insane.
That depends on the society, since "normal" and "crazy" are dictated by societal norms.

Of course, none of this really matters much. What's in my mind is all that matters - to me anyway - and that's all I really know.
Perhaps I'm reading this wrong, but that suggests a distinct lack of empathy and consideration for others.

[Strell]

Hello everyone.

I'm new to the boards in terms of posting. I lurk here and there, but never posted. This topic, however, caught my eye, so I thought I'd try my hand at a few of the problems here.

I will say that I have not read every reply to the fullest, so maybe I'm repeating people.

1. The limit of .99999999~ is, indeed, 1. But the limit does not equal the value. That's one of the first rules in calculus. The limit of a function and the value of a function are not the same thing and can be different. This can be seen in any equation where there is a hole. It's been a while since I've done calc, but you can have a perfectly valid function that "breaks down" somewhere and isn't continuous, thus never reaching a point. Take the equation 1/(x-2). At the point where x=2, the limit of the function is infinite. Coming from the left, it's negative inifinity, and from the right, positive. It has a limit, BUT it doesn't have a value. A rule of math is that you can't divide by zero. Hence the equation has a limit, but not a value. Therefore you can't assert that the limit of a function is it's value as well.

2. Additionally, you can't ever subtract infinity from infinity. That's not mathetically possible. You can't just say x = some infinite number and that x - x = 0. That's not logical at all. Just because we figuratively show them as representing the same thing by labelling them the same doesn't mean they necessarily are. The only way you could ever subtract infinity from infinity would be if both functions start from the exact same place and move at the exact same rate. You can't assume x = two different instances of infinity that are the same.

3. Things like 1/3 = .333 fall into the same realm as this, but the fact is that 1/3 is an irrational number - it repeats endlessly. Just like Pi. Therefore you can't just assume things like .333 * 3 = (1/3) * 3 = 1. We place a limit on them for a reason - because our foolish minds wouldn't be able to handle it. This is why we have a whole set of numbers called irrational numbers - they don't terminate.

4. As for the philosophical discussions, the fact of the matter is that, well, you can't be true of anything. There could always be what is referred to as an "evil demon" that subsequently controls the world and everything in it. Essentially we'd all be in the Matrix and never know it. Thus if everything was a false reality, we would never have true knowledge, and thus could never prove anything. Because we cannot eliminate this possibility, we can never truly be sure of anything. This is why philosophy is a load of bullshit and no one should waste their time with it. :) Argue about it all you want, and study philosophy all you want. All it ends up being is a waste of time because no one can definitively prove one thing and not another, which is why so many philosophers die alone, cold, and insane.

I am rusty on these subjects though. :)

Good day all.

[organicow]

4. As for the philosophical discussions, the fact of the matter is that, well, you can't be true of anything. There could always be what is referred to as an "evil demon" that subsequently controls the world and everything in it. Essentially we'd all be in the Matrix and never know it. Thus if everything was a false reality, we would never have true knowledge, and thus could never prove anything. Because we cannot eliminate this possibility, we can never truly be sure of anything. This is why philosophy is a load of bullshit and no one should waste their time with it. Argue about it all you want, and study philosophy all you want. All it ends up being is a waste of time because no one can definitively prove one thing and not another, which is why so many philosophers die alone, cold, and insane.

Yeah. We all know that the math geeks are the ones who get all the chicks, right?!? Not those silly philosophy nerds!!! \:D/

Actually, I find that one of the most frustrating similarities between math and philosophy is that they both have the nasty habit of presenting more questions than answers. They are also both very important, and they also both make my brain ache.

Ah, here's to friendly debate at CAG!!! :D

[ransom456]

1. The limit of .99999999~ is, indeed, 1. But the limit does not equal the value. That's one of the first rules in calculus. The limit of a function and the value of a function are not the same thing and can be different. This can be seen in any equation where there is a hole.


Err, .999... is not a function. It is a number. And it is equal to 1. Your recollection isn't totally off track, though. The number 0.999... is the limit of the sequence 0.9, 0.99, 0.999, 0.9999, ....
That sequence never actually achieves its limit.


3. Things like 1/3 = .333 fall into the same realm as this, but the fact is that 1/3 is an irrational number - it repeats endlessly. Just like Pi. Therefore you can't just assume things like .333 * 3 = (1/3) * 3 = 1. We place a limit on them for a reason - because our foolish minds wouldn't be able to handle it. This is why we have a whole set of numbers called irrational numbers - they don't terminate.


Actually, irrational numbers are those that cannot be represented as the ratio of two integers. So, for example, 1/3 is actually rational. Pi, as you say, is irrational. Irrational numbers have no repeating pattern to their decimal expansions.

As far as the more philosophical aspects of the discussion, GameDude and the others do have a point. Mathematics cannot prove absolutes. Mathematics needs assumptions (axioms, we call 'em) to build upon. So every mathematical statement is really an implication, like, "If we assume X, it follows that Y must hold." So if I am challenged to prove my existence, I would first need to know, "What am I allowed to assume?"

[ReussDr]

The world is flat. It's been mathamatically proven!

Well, that was the thought so many years ago. Just because something is mathmatically proven or thought so by the general scientific community, doesn't make it legit.

There are pink elephants with feathers.

Care to prove me wrong?

Ever do any work with Aristotlian Logic? In order to prove an argument, you have a number of premises, and those premises lead to a conclusion. When you want to attack someone's argument, you either point out that one of their premises is in fact wrong, or that the conclusion does not logically follow the premises.

From the base rules of mathematics, the conclusion stated in the original post is correct (errors in his steps not withstanding). Based on the laws of mathematics (the premises in this argument), it does logically follow. What you describe above are consequences on the real world, while this argument only discusses the fundamental principles of mathematics effects on it's own number system. What you instead need to do is research the principles of mathematics, and find which one of them you claim is incorrect. But since we're not concluding anything about the real world by saying that 1 = .9999~, it won't mean anything, because finding a flaw in a premise of Mathematics necessarily makes the number system flawed as well.

Sidenote: The notion that our ancestor's believed that the world is flat is likely incorrect, or at least vastly overestimated. It's popularized to make it seem that we have come a very far way in our understanding of the world, but it's doubted how much the educational elite actually believed it.

Also, to the person who posed the question of whether there are more real numbers or odd real numbers, it has been proven that some infities are larger than others, which is why infinity divided by infinity is inconclusive (you need more information). There are more real numbers than odd real numbers, though the answer to both is infinity.

[ElwoodCuse]

http://www.straightdope.com/columns/030711.html

here's some pretty good stuff

[Mr. Anderson]

Well, we're about 1/4 of the way to 200 post! Keep em' comin'! I'll just be in the corner hitting myself in the head with a hammer...

[digioverload]

Let X = .99999~

X = .9999~
10X = 9.999~
-1X = -1X (.999~)
9X = 9
X = 1

See?
I see it, but it's wrong.

.99~ does equal 1, but what you did does not prove that and actually uses incorrect math. There are several ways to prove it using real math, so I don't know why you've wasted your time using that. Common sense should have told you that it's wrong, but even if you have none, you should have caught it if you knew that infinity does not equal infinity minus 1.

Let me show you a few examples:

x = .99
10x = 9.9
10x - x = 9.9 - .99
9x = 8.91
x = .99

x = .999
10x = 9.99
10x - x = 9.99 - .999
9x = 8.991
x = .999

x = .99999
10x = 9.9999
10x - x = 9.9999 - .99999
9x = 8.99991
x = .99999

x = .99999999999999999999
10x = 9.9999999999999999999
10x - x = 9.9999999999999999999 - .99999999999999999999
9x = 8.99999999999999999991
x = .99999999999999999999

10x will always have 1 fewer decimal points than x. That will never change, even if you go somehow go all the way to infinity.

x = .<infinately many 9's>
10x = 9.<1 less than infinately many 9's>
10x - x = 9.<1 less than infinately many 9's> - .<infinately many 9's>
9x = 8.<1 less than infinately many 9's>1
x = .<infinately many 9's>

The reason this is true is because infinity does not equal infinity minus 1. If you don't believe me, you can go look it up yourself. The idea that they aren't equal is very basic and should have been taught to you in highschool. Because the decimal value of x does not equal the decimal value of 10x, your math is incorrect. x will always have one more decimal place (with a 9 in it) than 10x does.

You really shouldn't be trying to show people things that you don't understand. Next time you try to do this, use real math.

I understand that .99~ equals 1, that 9.99~ equals 10, and that 8.999~9991 equals 9. The problem is that what you've tried to use to prove it is wrong and doesn't prove anything excpet that x equals x.

Actually, that's all it would prove if you did it right. Since you did it wrong, it doesn't prove anything.

[GameDude]

The world is flat. It's been mathamatically proven!

Well, that was the thought so many years ago. Just because something is mathmatically proven or thought so by the general scientific community, doesn't make it legit.

There are pink elephants with feathers.

Care to prove me wrong?

Ever do any work with Aristotlian Logic? In order to prove an argument, you have a number of premises, and those premises lead to a conclusion. When you want to attack someone's argument, you either point out that one of their premises is in fact wrong, or that the conclusion does not logically follow the premises.

From the base rules of mathematics, the conclusion stated in the original post is correct (errors in his steps not withstanding). Based on the laws of mathematics (the premises in this argument), it does logically follow. What you describe above are consequences on the real world, while this argument only discusses the fundamental principles of mathematics effects on it's own number system. What you instead need to do is research the principles of mathematics, and find which one of them you claim is incorrect. But since we're not concluding anything about the real world by saying that 1 = .9999~, it won't mean anything, because finding a flaw in a premise of Mathematics necessarily makes the number system flawed as well.

Sidenote: The notion that our ancestor's believed that the world is flat is likely incorrect, or at least vastly overestimated. It's popularized to make it seem that we have come a very far way in our understanding of the world, but it's doubted how much the educational elite actually believed it.

Also, to the person who posed the question of whether there are more real numbers or odd real numbers, it has been proven that some infities are larger than others, which is why infinity divided by infinity is inconclusive (you need more information). There are more real numbers than odd real numbers, though the answer to both is infinity.

First off, I don't believe I ever said he was wrong. I simply said that he might not be right. I said it's impossilbe to prove or disprove anything - all we know and all we are is in our head - a biased contraption for sure...or is it?

[JSweeney]

It's the view of a philosopher. I much perfer the view of the scientist.

If you hold to the idea that proving or disproving is impossible, you must divorce yourself mathematics, logic, and science itself.
All of these fields are primarily based upon the ability to formulate a hypothesis or thesis, and through use of examination, experimentation, and prediction prove thier validity.

I said it's impossilbe to prove or disprove anything - all we know and all we are is in our head


Not exactly. If that were true, one should be able to distort the natural order of the universe to the specifications that exist in one's own mind...yet gravity and other natural laws still hold sway.

If all you know and all you are is your mind, then why can you not overcome hunger? If everything was in your mind, you should be able to think "I'm not hungry" and your body would be satisfied. But that doesn't work.. If you do that, you will begin to starve, and your body will begin to eat itself.

[GameDude]

It's the view of a philosopher. I much perfer the view of the scientist.

If you hold to the idea that proving or disproving is impossible, you must divorce yourself mathematics, logic, and science itself.
All of these fields are primarily based upon the ability to formulate a hypothesis or thesis, and through use of examination, experimentation, and prediction prove thier validity.

I said it's impossilbe to prove or disprove anything - all we know and all we are is in our head


Not exactly. If that were true, one should be able to distort the natural order of the universe to the specifications that exist in one's own mind...yet gravity and other natural laws still hold sway.

If all you know and all you are is your mind, then why can you not overcome hunger? If everything was in your mind, you should be able to think "I'm not hungry" and your body would be satisfied. But that doesn't work.. If you do that, you will begin to starve, and your body will begin to eat itself.

How do I know if I'm really eating anything? How do I know if I'm not floating? I can't prove or disprove it. Everything I interpret is through my mind. You can't prove that you're not an insane person...this whole "reality" may just be in your head. I'm not saying this is true, because if I thought it were true, I'd be insane. :wink:

[magilacudy]

Ok, I see what you're trying to prove, Gamedude. You're trying to give us the text form of a red pill. There is no spoon! We're in the Matrix!

What you're trying to say nothing is proveable i.e. all in your head, so what's the point of trying to prove a point? There is none according to your logic.

You are right, though, you are insane. No I'm not going to back that up with anything, I'm just saying that as an opinion. =P

[zin63]

guys, guys, don't fight - can't we just agree to disagree?

no, but really, who brought philosophy into this? the epic battle between JSweeney and GameDude is a battle between ideologies, and it's also really unnecessary. I agree with both of you (really) but you both seem to be on different levels of reasoning. GameDude is all about subjectivity and whatever- this is rooted in psychology and philosophy. JSweeney, I think you should accept the fact that nothing is absolute. BUT- after you accept that, there's the whole idea of relativity (not Einstein's, just literal). TO YOU (and to those who agree, myself included), based on the axioms that society is based on, the current state of mathematics IS infallible, because it is always correct in its field of expertise. It WORKS in our society, even if it is false in another, and therefore its ideas are true because they have been proven in our plane of existance. Regardless of how real or important our existance is, there are a set of truths it accepts. Anyone hear of anthropic principle? It's kind of related. 0.999.... is equal to 1, because it uses a certain set of numbers and ideas that have been proven in its plane of existance. In another plane of exisance, what importance do foreign numbers or ideas have anyway? And vice-versa, what importance do numbers and ideas from another plane of existance have in ours?

[JSweeney]

[quote=JSweeney]It's the view of a philosopher. I much perfer the view of the scientist.

If you hold to the idea that proving or disproving is impossible, you must divorce yourself mathematics, logic, and science itself.
All of these fields are primarily based upon the ability to formulate a hypothesis or thesis, and through use of examination, experimentation, and prediction prove thier validity.

I said it's impossilbe to prove or disprove anything - all we know and all we are is in our head


Not exactly. If that were true, one should be able to distort the natural order of the universe to the specifications that exist in one's own mind...yet gravity and other natural laws still hold sway.

If all you know and all you are is your mind, then why can you not overcome hunger? If everything was in your mind, you should be able to think "I'm not hungry" and your body would be satisfied. But that doesn't work.. If you do that, you will begin to starve, and your body will begin to eat itself.

How do I know if I'm really eating anything?

The tastebuds in your tounge transmit information through your body which is then translated by your brain, and relays either a positive or negative sensation, making it pleasurable or unpleasurable.

Beyond that, you will no if you are eating or not eating by body function.
The mind, as much as people want to talk it up is still but part of a system, and is worthless without it's related functions. The mind cannot exist without the body, unless you perscribe to the view that the mind is the soul.


How do I know if I'm not floating?
The body has a sense of orination. If you were floating, the body would transmit to the mind that sense of disorintation... even if you didn't know what that was. The mind would notice something was wrong due to the mind/body link.


I can't prove or disprove it. Everything I interpret is through my mind.
Iterpret, yes, but not sense. There are even schools of thought that believe that there are parts of the subconcious mind that deal with this sensory information, therefor the mind itself knows reality, even if the concious ego does not.



You can't prove that you're not an insane person...
Yes you can. You may not be able to prove it to others, but you can prove it to yourself. Insanity isn't even a good example, because the boundaries sanity are determined by societal norms. Even if your reality is just in your mind, your sanity would be detrimined by the societal structure in your imagined realm. Sanity is not an absolute.




this whole "reality" may just be in your head. I'm not saying this is true, because if I thought it were true, I'd be insane.

Even if it were, there would still be rules and laws by which knowledge could be dervived and proven from. If it's actually real or not doesn't matter. Things could still be proven to a certainy and concensus from your frame of reference. Pondering wheter or not your frame of reference is the proper one is a rather futile effort, as everything you are going to say is going to hinge on belief.

Trying to figure out if something is absolutely true is a worthless endeavor. It really doesn't matter, as the knowledge is worthless if you are still constrained in the same system, and will still be judged by the rules inherent to that system.

We don't have to prove things absolutely true. All we have to do is show them to be replicable and provide a plausible hypothesis for explaining. If new knowledge comes along that shows us that we misunderstood something, we amend our hypothesis.

It's better to seek out knowledge and strive for truth and understanding that to just say " why bother, it's impossible to prove anything anyway."

It much rather use knowledge and concepts as tools, and view things scientifically rather than to view things as "toy problems" to be tinkered with and viewed philosophically. I know this view is considered small minded, and particularly scorned by philosophers, but I don't really care. If I'm going to accept philosophy based on nothing but faith and belief, I'll take religious philosophy any day over the psuedo-scientific "pop philosophy" any day.

[CaptainObviousXl]

.99999~= 1 does it even matter, prove me wrong.

[JSweeney]

.99999~= 1 does it even matter, prove me wrong.

If you plan to take higher level mathematics, yes.
If you plan to dig ditches or flip hamburger patties the rest of your life..
no.

[magilacudy]

That's what I love about philosophy. After all is said and done, more was said than done. You can theorize and argue all day about whether something exists absolutely in any number of planes, but when it comes down to it there's still an equation (that was the point of the thread after all) that needs to be solved or work that needs to be done.

A bunch of hooey I tells ya. I'm an engineer, and those were my 2 cents.

[JSweeney]

That's what I love about philosophy. After all is said and done, more was said than done. You can theorize and argue all day about whether something exists absolutely in any number of planes, but when it comes down to it there's still an equation (that was the point of the thread after all) that needs to be solved or work that needs to be done.

A bunch of hooey I tells ya. I'm an engineer, and those were my 2 cents.

I think that's the major problem here magilacudy... we're scientists.
Scientists and Philosophers can never seem to come to terms... both seek to explain the unexplained, but due to the drastic difference in thier approaches to doing so, rifts often come up.

Philosophical methods aren't so easily explained as the scientific method.

[eldad9]

http://mathforum.org/dr.math/faq/faq.0.9999.html

[JSweeney]

guys, guys, don't fight - can't we just agree to disagree?
There's a differnce between a fight and a argument/discourse.
Thanks to the realitively high level of decorum we've been posting with, it hasn't crossed the threshold to being a fight.

no, but really, who brought philosophy into this? the epic battle between JSweeney and GameDude is a battle between ideologies, and it's also really unnecessary.

I think the biggest rift is that both of us aren't being clear enough. I've never be talking about absolutes.. and thier is a difference between proof to a certainty and proof to an absolute. It's just that I never explicitly pointed out that fact. That's the biggest point of contention here. I argee with him to a point if we are only talking about absolute truths. But neither of us explicitly said at any point that we were discusing absolute truths or absolutely proving anything.


I agree with both of you (really) but you both seem to be on different levels of reasoning. GameDude is all about subjectivity and whatever- this is rooted in psychology and philosophy. JSweeney, I think you should accept the fact that nothing is absolute.

I don't accept the fact that NOTHING is absolute, but I do accept the fact that to be able to prove things absolutely is beyond our (humanity) capacity.



BUT- after you accept that, there's the whole idea of relativity (not Einstein's, just literal). TO YOU (and to those who agree, myself included), based on the axioms that society is based on, the current state of mathematics IS infallible, because it is always correct in its field of expertise. It WORKS in our society, even if it is false in another, and therefore its ideas are true because they have been proven in our plane of existance. Regardless of how real or important our existance is, there are a set of truths it accepts. Anyone hear of anthropic principle? It's kind of related. 0.999.... is equal to 1, because it uses a certain set of numbers and ideas that have been proven in its plane of existance. In another plane of exisance, what importance do foreign numbers or ideas have anyway? And vice-versa, what importance do numbers and ideas from another plane of existance have in ours

Exactly. That's been the crux of just about all of my posts. While we don't have the capacity to prove absolute truths, we do have the capacity to prove relative truths. But, if we can prove relative truths, and proving things IS possible.

The biggest problem in this argument has been the specification of terms, just as you said.

[oNeWiNgEdAnGeL]

Let X = .99999~

X = .9999~
10X = 9.999~
-1X = -1X (.999~)
9X = 9
X = 1

See?

I asked my teacher this when I saw someone post this at another message board, and he did the same exact thing you posted.

But I'm the kind of person that just can't seem to see [i]why[/b] that should work. If 1/3 = .33~, 2/3 = 66~, then 3/3 should = .99~. But we all know 3/3 = 1.

I think we need Scooyd-Doo and the gang to solve this mystery!

[GameDude]

guys, guys, don't fight - can't we just agree to disagree?
There's a differnce between a fight and a argument/discourse.
Thanks to the realitively high level of decorum we've been posting with, it hasn't crossed the threshold to being a fight.

no, but really, who brought philosophy into this? the epic battle between JSweeney and GameDude is a battle between ideologies, and it's also really unnecessary.

I think the biggest rift is that both of us aren't being clear enough. I've never be talking about absolutes.. and thier is a difference between proof to a certainty and proof to an absolute. It's just that I never explicitly pointed out that fact. That's the biggest point of contention here. I argee with him to a point if we are only talking about absolute truths. But neither of us explicitly said at any point that we were discusing absolute truths or absolutely proving anything.


I agree with both of you (really) but you both seem to be on different levels of reasoning. GameDude is all about subjectivity and whatever- this is rooted in psychology and philosophy. JSweeney, I think you should accept the fact that nothing is absolute.

I don't accept the fact that NOTHING is absolute, but I do accept the fact that to be able to prove things absolutely is beyond our (humanity) capacity.



BUT- after you accept that, there's the whole idea of relativity (not Einstein's, just literal). TO YOU (and to those who agree, myself included), based on the axioms that society is based on, the current state of mathematics IS infallible, because it is always correct in its field of expertise. It WORKS in our society, even if it is false in another, and therefore its ideas are true because they have been proven in our plane of existance. Regardless of how real or important our existance is, there are a set of truths it accepts. Anyone hear of anthropic principle? It's kind of related. 0.999.... is equal to 1, because it uses a certain set of numbers and ideas that have been proven in its plane of existance. In another plane of exisance, what importance do foreign numbers or ideas have anyway? And vice-versa, what importance do numbers and ideas from another plane of existance have in ours

Exactly. That's been the crux of just about all of my posts. While we don't have the capacity to prove absolute truths, we do have the capacity to prove relative truths. But, if we can prove relative truths, and proving things IS possible.

The biggest problem in this argument has been the specification of terms, just as you said.

Let's say that you can prove something. Who are you proving it to? Yourself? EVERYTHING is an interpretation from your mind; your whole being. Sure, you may "prove" to yourself that smoking improves your health, but that doesn't mean that's true.

Does society really determine if someone is insane? Or are you? I bet that person who is considered insane doesn't think so. But who's right? Who's wrong? There is no right or wrong.

The freedom fighters killed the evil Americans.
The terrorists killed the upright Americans.

Who's right? Of course YOUR opinion is right, and mine is wrong...if this weren't true, you wouldn't believe in your opinion.

I think you're just missing my point, because what I'm trying to say is quite simple to grasp. You prove something to someone predicated on what you think. The person your proving it to is there, but perhaps only in your mind...and there's nothing you could do to prove otherwise. Why? Because everything you are, were, and ever will be is in that noggin of yours.

[ransom456]

.99~ does equal 1, but what you did does not prove that and actually uses incorrect math. There are several ways to prove it using real math, so I don't know why you've wasted your time using that. Common sense should have told you that it's wrong, but even if you have none, you should have caught it if you knew that infinity does not equal infinity minus 1.

Let me show you a few examples:

x = .99
10x = 9.9
10x - x = 9.9 - .99
9x = 8.91
x = .99

x = .999
10x = 9.99
10x - x = 9.99 - .999
9x = 8.991
x = .999

x = .99999
10x = 9.9999
10x - x = 9.9999 - .99999
9x = 8.99991
x = .99999

x = .99999999999999999999
10x = 9.9999999999999999999
10x - x = 9.9999999999999999999 - .99999999999999999999
9x = 8.99999999999999999991
x = .99999999999999999999

10x will always have 1 fewer decimal points than x. That will never change, even if you go somehow go all the way to infinity.

x = .<infinately many 9's>
10x = 9.<1 less than infinately many 9's>
10x - x = 9.<1 less than infinately many 9's> - .<infinately many 9's>
9x = 8.<1 less than infinately many 9's>1
x = .<infinately many 9's>

The reason this is true is because infinity does not equal infinity minus 1. If you don't believe me, you can go look it up yourself. The idea that they aren't equal is very basic and should have been taught to you in highschool. Because the decimal value of x does not equal the decimal value of 10x, your math is incorrect. x will always have one more decimal place (with a 9 in it) than 10x does.

You really shouldn't be trying to show people things that you don't understand. Next time you try to do this, use real math.

I understand that .99~ equals 1, that 9.99~ equals 10, and that 8.999~9991 equals 9. The problem is that what you've tried to use to prove it is wrong and doesn't prove anything excpet that x equals x.

Actually, that's all it would prove if you did it right. Since you did it wrong, it doesn't prove anything.

I don't know what high school you went to, but pretty much everything you said is wrong. If you have an infinite number of decimal places, and you take one away, there are still an infinite number of decimal places. The cardinality of a countably infinite set and that of a set containing one fewer element are the same.

The argument the OP gave is correct. It basically has embedded within it the proof of the formula for the sum of an infinite geometric series.

[CaptainObviousXl]

.99999~= 1 does it even matter, prove me wrong.

If you plan to take higher level mathematics, yes.
If you plan to dig ditches or flip hamburger patties the rest of your life..
no.
ummmmm u dont think i need this even for a highrer levels of mathmatics, also i am the 4th highest scoring math student on the a exam in our school
out of like 250 others who took this

[JSweeney]

.99999~= 1 does it even matter, prove me wrong.

If you plan to take higher level mathematics, yes.
If you plan to dig ditches or flip hamburger patties the rest of your life..
no.
ummmmm u dont think i need this even for a highrer levels of mathmatics, also i am the 4th highest scoring math student on the a exam in our school
out of like 250 others who took this

You obviously haven't taken calculus then.
Wow, your the 4th highest scoring math student in your school. We'll definately take your word over the guy who posted a couple of pages back who's getting a PHD in math, or the myraid of computer scientists and engineers posting in this thread.

[JSweeney]

Let's say that you can prove something. Who are you proving it to? Yourself? EVERYTHING is an interpretation from your mind; your whole being. Sure, you may "prove" to yourself that smoking improves your health, but that doesn't mean that's true.

Proof, in the relative sense, you prove to yourselves and others.
In the absolute sense, if you even could, you could only prove it to yourself.
Not everything is interpretation by your mind. In the sense you are using it, Mind is only the concious aspect of the mind, and not the subconcious or even physical parts of the brain itself. As they are all parts of a system, they can not function without each other... unless, as I stated before, you hold the belief that the mind is the soul.

Does society really determine if someone is insane?
Yes, because sanity is decided based upon adherence to societal norms.
You don't dictate the norms... society does.


Or are you?
If you are determining yourself to be insane, you must have a set standard in your mind that you deviate from. If that's the case, where did the stadards come from? More likely than not, the answer is society.

I bet that person who is considered insane doesn't think so. But who's right? Who's wrong? There is no right or wrong.

Since it is society that is laying down the rules, it is. It's doesn't matter if they are absolutely correct.. since they decided the rules and norms that dictate how individuals in a society function, thier decision is correct, even if it is just a relative truth.


The freedom fighters killed the evil Americans.
The terrorists killed the upright Americans.

Two different societies. To different sets of social norms. In each society, based on the relative truths that they hold to, both statements are correct.
Which is absolutely correct? Niether. We (humanity) don't have the capacity to decide that.


Who's right? Of course YOUR opinion is right, and mine is wrong...if this weren't true, you wouldn't believe in your opinion.

Both. and Neither. Relative truths can be found based on the rules and stuctures devised by the society in which one exists.


I think you're just missing my point, because what I'm trying to say is quite simple to grasp.

You are oversimplifying. While you may be correct in the sense of absolute truth, you are radically incorrect in the sense of relative truth.
Both exist, and can exist independantly of each other... but to mention one without addressing or agreeing the existance of the other is terribly negligent.


You prove something to someone predicated on what you think.
This is a relative truth. You forumlate it based upon your experience and the bais of the society in which you live.

The person your proving it to is there, but perhaps only in your mind...and there's nothing you could do to prove otherwise.
In the absolute sense, yes, you couldn't. But in the relative sense, you could show that they have life signs, a conciousness of thier own, and many other examples proving that they do , in fact, exist.


Why? Because everything you are, were, and ever will be is in that noggin of yours.

Wrong. If you're going to argue the value of the mind, you can't just ignore the value and importance of the soul. If you're going to go beyond science and tread in the ground of the supernatural, you can't neglect the concept of the soul.

[sTaTIx]

JSweeney, let me ask you: what if CheapAssGamer.com is a figment of your imagination? What if GameDude and I are figments of your imagination? What if everything you know or think you know to be true is just a illusion, including your knowledge of mathematics and the number system, and does not exist for any other being in the universe?

[ReussDr]

That's what I love about philosophy. After all is said and done, more was said than done. You can theorize and argue all day about whether something exists absolutely in any number of planes, but when it comes down to it there's still an equation (that was the point of the thread after all) that needs to be solved or work that needs to be done.

A bunch of hooey I tells ya. I'm an engineer, and those were my 2 cents.

I think that's the major problem here magilacudy... we're scientists.
Scientists and Philosophers can never seem to come to terms... both seek to explain the unexplained, but due to the drastic difference in thier approaches to doing so, rifts often come up.

Philosophical methods aren't so easily explained as the scientific method.

No way am I giving you that conclusion without an argument...

As someone with a Bachelor's Degree in Computer Science and a minor in Philosophy, you're pretty far off base there. Would you say that Descartes, Aristotle, Plato, and Leibniz were Philosophers or Scientists?

Philosophers who use the "I'm not really here" approach are somewhat ridiculous. You can't actually use it as a stepping stone for anything else, so it's a pointless exercise. What Descartes did was to take the approach of a complete skeptic, and go down to the only thing he couldn't doubt... His own existence. After all, even if you really did believe that you don't exist, why would you bother to get up in the morning, consume food, go about your daily business, or respond to posts on a message board. It'd all be pointless, right? To my knowledge, no philosopher has ever died from wasting away to nothing because he ceased to continue to get out of bed in the morning.

Having studied logic as taught (seperately) by Computer Scientists, Electrical Engineers, and Philosophers, there is a difference in methodology, but the rule system is effectively the same (all derived from Aristotlian logic). None of them will let you prove P & ~P (that boolean variable P is both true and false at the same time).

Any philsopher trying to make an argument without an understanding of logic will have his ass handed to him. You simply need logic to make a valid conclusion based on your premises. The "methods" of Philosophy are just as easily explained as those of Mathematics or Science.

That said, most Philosophical arguments are purely mental exercises. The exchanges between philosophers never question the rules for forming an argument and proving it to be valid. Instead, they attack the premises, or the steps taken to arrive at the conclusion (and note that a particular step violated the rules of Logic).

[magilacudy]

A couple of points served up JSweeney style:

1) If that is true that we are but figments of someone's imagination, then that God forbid if that person were to go into a coma or die - - then we all would cease to exist. Anyone care to test that theory?

2) What if someone was to go to your house, rape your parents, kill your pets and burn your house down. Would that be wrong? According to Gamedude's theory, it is not, and can't be judged by our society.

Unless you draw the line somewhere, society (even if it is just in your head) would fall apart. That goes for mathemetics as well, even though I doubt you still remember that was the original post.

3) Opinions are not inherently right, or wrong. They are opinions. If you had the opinion that Morgan Webb was the hottest girl in the world, that would be neither right or wrong, only a opinion (sorry just came to mind hehe). Just because it is YOUR opinion does not have any bearing on the validity of the statement. Hence the relativity.

3) That link to that math site cleared everything up for the most part.

4) Gamedude, were you in my philosophy class last semester? My prof made most of these same arguments you were making, but he showed the flaws in them the next class. Maybe you were absent that day.

5) Philosophers should stick to philosophy, mathmeticians should stick to math, or whatever job you have should stick to debating the expertise in that field. I think it was Socrates who stated that and was killed for it.

6) Now I see how this could reach 200 posts in Gamefaqs.

[JSweeney]

JSweeney, let me ask you: what if CheapAssGamer.com is a figment of your imagination? What if GameDude and I are figments of your imagination? What if everything you know or think you know to be true is just a illusion, including your knowledge of mathematics and the number system, and does not exist for any other being in the universe?

So long if I believe that CAG is true, and that is a relative truth to me, the absolute truth (the situation which you state) doesn't really matter to me.. as my relative truth is what dicates my reality and not absolute truth.

[magilacudy]

No way am I giving you that conclusion without an argument...

I think JSweeney wasn't saying that the logic was any different. You are coming to the same conclusion of the drastic differences as he did, maybe you don't realize it though. Simply put, mathemetics/science questions the how, while philosophy questions the why... *picturing Peter Griffin's ancestor the philosopher*. Yes, logic is needed in both, but what is done with it is the fundamental difference between the two.

[JSweeney]

That's what I love about philosophy. After all is said and done, more was said than done. You can theorize and argue all day about whether something exists absolutely in any number of planes, but when it comes down to it there's still an equation (that was the point of the thread after all) that needs to be solved or work that needs to be done.

A bunch of hooey I tells ya. I'm an engineer, and those were my 2 cents.

I think that's the major problem here magilacudy... we're scientists.
Scientists and Philosophers can never seem to come to terms... both seek to explain the unexplained, but due to the drastic difference in thier approaches to doing so, rifts often come up.

Philosophical methods aren't so easily explained as the scientific method.

No way am I giving you that conclusion without an argument...

As someone with a Bachelor's Degree in Computer Science and a minor in Philosophy, you're pretty far off base there. Would you say that Descartes, Aristotle, Plato, and Leibniz were Philosophers or Scientists?

They were both. It is possible to be both a philosopher and a scientist.. some of the greatest scientist ever were also renoun philosophers. I'm not meaning to talk down the entire field of philosophy with that statement... just the modern brand of pop philosophy... the same type of philosophy that compains about absolute truths, yet fails to accept the plausablilty of theology.

Philosophers who use the "I'm not really here" approach are somewhat ridiculous. You can't actually use it as a stepping stone for anything else, so it's a pointless exercise. What Descartes did was to take the approach of a complete skeptic, and go down to the only thing he couldn't doubt... His own existence. After all, even if you really did believe that you don't exist, why would you bother to get up in the morning, consume food, go about your daily business, or respond to posts on a message board. It'd all be pointless, right? To my knowledge, no philosopher has ever died from wasting away to nothing because he ceased to continue to get out of bed in the morning.

You're not going to get an argument from me on this. I've already used part of this agrument against GameDude. Agruing something similar to what I stated would be fruitless.

Having studied logic as taught (seperately) by Computer Scientists, Electrical Engineers, and Philosophers, there is a difference in methodology, but the rule system is effectively the same (all derived from Aristotlian logic). None of them will let you prove P & ~P (that boolean variable P is both true and false at the same time).

Again, very true. Perhap's it's just that most of the people I've talked with are not truly philosopher's but rather people who've come up with this little toy concept in thier head, and then proceed to agrue it despite not having an understanding of the logic underlying it.


Any philsopher trying to make an argument without an understanding of logic will have his ass handed to him. You simply need logic to make a valid conclusion based on your premises. The "methods" of Philosophy are just as easily explained as those of Mathematics or Science.

Again, more likely that not this is just me making a misinterpretation based on the usage of philosophical concepts by people in everyday conversation or on message boards. All of the logic I've ever been taught was through Comptuer Science, and most of my other coursework was in other branches of science.


That said, most Philosophical arguments are purely mental exercises. The exchanges between philosophers never question the rules for forming an argument and proving it to be valid. Instead, they attack the premises, or the steps taken to arrive at the conclusion (and note that a particular step violated the rules of Logic).

That's probably my biggest sticking point. I'm so used to the usage of the scientific method, and the set rules for even establishing hypothesis that a school of thought where the rules of forming a case are trivial just seems a bit off to me.

[chunk]

The idiocy in this thread is absolutely incredible.

.9999~ does in fact equal one. However, there are numbers that are closer to 1 than any other number. If you really want to know, then study some non-standard calculus using the hyperreal or surreal sets of numbers. These make much more sense than your standard set of "real numbers" which are a real hackjob when it comes to infinities and infintesimals. Look for more information at www.wikipedia.com

Of course everyone always should remember that mathematics never proves anything. All it says is that if one thing is true then something else is also true. Ironically mathematical proofs are the closest thing you can get to proving that something is actually true.

P.S. Enough with the philosophy....lets talk mathematics!

[Quackzilla]

if you take an object, and keepp cutting off 90% of it, will it eventually dissapear? (pretend that it is just solid stuff, not particles)

[ReussDr]

if you take an object, and keepp cutting off 90% of it, will it eventually dissapear? (pretend that it is just solid stuff, not particles)

Yes and No (depending on your definition of "eventually", Merriam Webster confirms that it can be used to describe either of the definitions detailed below)... Let's look to Calculus to solve this

You're looking at the function "Y = .1^X". The limit of Y as X approaches positive infinity is 0. That is to say, that the % of the object remaining (Y) approaches 0 as time (X) approaches infinity. At infinity it is 0, but at any discrete point in time, there is some amount of object remaining (assuming you don't round off to the nearest Quark). If you mean eventually to be some discrete point in the future, then no. If you mean eventually to be an infinite amount of time later, then yes.

[ReussDr]

if you take an object, and keepp cutting off 90% of it, will it eventually dissapear? (pretend that it is just solid stuff, not particles)

Yes and No (depending on your definition of "eventually", Merriam Webster confirms that it can be used to describe either of the definitions detailed below)... Let's look to Calculus to solve this

You're looking at the function "Y = .1^X". The limit of Y as X approaches positive infinity is 0. That is to say, that the % of the object remaining (Y) approaches 0 as time (X) approaches infinity. At infinity it is 0, but at any discrete point in time, there is some amount of object remaining (assuming you don't round off to the nearest Quark). If you mean eventually to be some discrete point in the future, then no. If you mean eventually to be an infinite amount of time later, then yes.

[chunk]

if you take an object, and keepp cutting off 90% of it, will it eventually dissapear? (pretend that it is just solid stuff, not particles)

Yes and No (depending on your definition of "eventually", Merriam Webster confirms that it can be used to describe either of the definitions detailed below)... Let's look to Calculus to solve this

You're looking at the function "Y = .1^X". The limit of Y as X approaches positive infinity is 0. That is to say, that the % of the object remaining (Y) approaches 0 as time (X) approaches infinity. At infinity it is 0, but at any discrete point in time, there is some amount of object remaining (assuming you don't round off to the nearest Quark). If you mean eventually to be some discrete point in the future, then no. If you mean eventually to be an infinite amount of time later, then yes.

Why can't infinity be a discrete point?

[zin63]

if you take an object, and keepp cutting off 90% of it, will it eventually dissapear? (pretend that it is just solid stuff, not particles)

Yes and No (depending on your definition of "eventually", Merriam Webster confirms that it can be used to describe either of the definitions detailed below)... Let's look to Calculus to solve this

You're looking at the function "Y = .1^X". The limit of Y as X approaches positive infinity is 0. That is to say, that the % of the object remaining (Y) approaches 0 as time (X) approaches infinity. At infinity it is 0, but at any discrete point in time, there is some amount of object remaining (assuming you don't round off to the nearest Quark). If you mean eventually to be some discrete point in the future, then no. If you mean eventually to be an infinite amount of time later, then yes.

Why can't infinity be a discrete point?

because a discreet point is a measurable quantum

[GameDude]

I'm not going to read all of that, because I don't really care that much.

I took philosophy in college for about a week, then dropped it.

As for the killer, though. To me, he is wrong and evil. However, in his mind, he may have been doing the work of some religious deity or something like that.

Yes, there are moral rights and wrongs judged by society - it's basically called "law." However, if you have a society of killers, killing wouldn't necessarily be thought of as wrong. Which society is right and which is wrong?

To me, the society of killers is evil and wrong, but, that is my opinion and not an absolute.

[magilacudy]

In a society where murder was not thought as of wrong, eventually you'd have a point where everyone would kill each other. There would be nothing stopping them from doing so -- leading to no society period.

Its called Hobbes' State of Nature dawg. Look it up. That's is why there are no societies where murder is considered right. There are moral absolutes, whether you want to acknowledge them or not, as there are mathemetical absolutes as well.

[hormoden]

i have done a thorough analysis of every comment and input, and my solution to this conundrum is: everybody be quiet. [-X

can you prove me wrong?
:mrgreen:

[magilacudy]

Nice pic horm.

[ReussDr]

ReussDr: As someone with a Bachelor's Degree in Computer Science and a minor in Philosophy, you're pretty far off base there. Would you say that Descartes, Aristotle, Plato, and Leibniz were Philosophers or Scientists?

JSweeney: They were both. It is possible to be both a philosopher and a scientist.. some of the greatest scientist ever were also renoun philosophers. I'm not meaning to talk down the entire field of philosophy with that statement... just the modern brand of pop philosophy... the same type of philosophy that compains about absolute truths, yet fails to accept the plausablilty of theology.

Well, I'm willing to forgive them for their trespass. After all, in order to keep the dialog going you have to have new intellectual heavy weights getting involved in the discourse, and most of the time that means criticizing some ancient but accepted figure.

ReussDr: Any philsopher trying to make an argument without an understanding of logic will have his ass handed to him. You simply need logic to make a valid conclusion based on your premises. The "methods" of Philosophy are just as easily explained as those of Mathematics or Science.

JSweeney: Again, more likely that not this is just me making a misinterpretation based on the usage of philosophical concepts by people in everyday conversation or on message boards. All of the logic I've ever been taught was through Comptuer Science, and most of my other coursework was in other branches of science.

Well, somewhere along the way, people got the impression that Philosophers sit around and smoke pot and pontificate on strange and wacky alternatives to how things really are. Real Philosophers engage in very complex arguments that tend to be extremely well thought out. Unlike an engineer or a doctor, there's no diploma or certification to state that you are in fact qualified to do such work, so many people claim to be the real thing when they are not.

ReussDr: That said, most Philosophical arguments are purely mental exercises. The exchanges between philosophers never question the rules for forming an argument and proving it to be valid. Instead, they attack the premises, or the steps taken to arrive at the conclusion (and note that a particular step violated the rules of Logic).

JSweeney: That's probably my biggest sticking point. I'm so used to the usage of the scientific method, and the set rules for even establishing hypothesis that a school of thought where the rules of forming a case are trivial just seems a bit off to me.

I don't understand that complaint. The rules for the Scientific Method are pretty simple, so that you can get on to the interesting work of coming up with a hypothesis and then testing it. The rules for making an argument are likewise very simple so you can get past the groundwork, and instead concentrate your efforts on coming up with a good argument, working your way to it's conclusion, and coming up with a good way to articulate that argument. In both cases the rules are very simplistic, because they're merely a guide to get you to the actual work.

[Mr. Anderson]

There are waaaaay too many smart people on this board....me not being one of them.

[JSweeney]

Well, I'm willing to forgive them for their trespass. After all, in order to keep the dialog going you have to have new intellectual heavy weights getting involved in the discourse, and most of the time that means criticizing some ancient but accepted figure.

True, but throwing a bulk of accepted works into a questionable nether-region just to advance your own theory is dangerous. I'd figure that only a few truely giften people could actually get away with doing that and not doing irrepaiable damage to thier own image and career. (Since there is no real burden that one must surpass to call themselves a philosopher).
I'm still rather offput by the disdain that some philosophers hold for theologists, all the while trying to build themselves up.
Theology is just a valid a school of thought, yet always seems to get put on the backburner... with the students of it maligned as nothing but "fanatics" or "blinded by thier religion".


Well, somewhere along the way, people got the impression that Philosophers sit around and smoke pot and pontificate on strange and wacky alternatives to how things really are.

Well, some of that is media perception, and some of that is the people on the internet who've taken one course in philosophy (or even a couple weeks) and pick up the mantle of the philospoher for themselves.

Real Philosophers engage in very complex arguments that tend to be extremely well thought out.

I know. I've read some of the works of philosophy.. and most of them are built from a simple stucture of stating logical premises and explaining and steping through them. If everyone who called themselves a philosopher acted as such, I'd be happy.

Unlike an engineer or a doctor, there's no diploma or certification to state that you are in fact qualified to do such work, so many people claim to be the real thing when they are not.

Very true. That's problem the biggest point of contention between us, and the cause of the perhaps irrational bias I formed against modern Philosophy.. thanks to the misqouting of modern philosophers and irresposible bearing of the mantle of philosopher, I've been jaded to the more logical, formalized brand of philosophy... the way philosophy was intented to be studied.



I don't understand that complaint. The rules for the Scientific Method are pretty simple, so that you can get on to the interesting work of coming up with a hypothesis and then testing it. The rules for making an argument are likewise very simple so you can get past the groundwork, and instead concentrate your efforts on coming up with a good argument, working your way to it's conclusion, and coming up with a good way to articulate that argument. In both cases the rules are very simplistic, because they're merely a guide to get you to the actual work.

I was still working off that same incorrect bias. Looking back at an old philosophy text, and then looking at a couple of other real works (and not the self proclaimed internet philosopher's diatribes) I realized I was wrong in making that statement. Real philosophers and philosophic works are laid out very specifically, often with the author offering up his contention, logically proving it's validity, and then even offering up and discrediting logically it's counter-points and con arguments.

[CaptainObviousXl]

.99999~= 1 does it even matter, prove me wrong.

If you plan to take higher level mathematics, yes.
If you plan to dig ditches or flip hamburger patties the rest of your life..
no.
ummmmm u dont think i need this even for a highrer levels of mathmatics, also i am the 4th highest scoring math student on the a exam in our school
out of like 250 others who took this

You obviously haven't taken calculus then.
Wow, your the 4th highest scoring math student in your school. We'll definately take your word over the guy who posted a couple of pages back who's getting a PHD in math, or the myraid of computer scientists and engineers posting in this thread.
take my wordabout wat, im just saying that math is my best subjct, dont flip out on me.

[tsheo]

X9=9 this will only be true if your some how asuming that X=1 not .99~. .99~ isn't areal number so it can go either way for practicle purposes use .99999.... for theoretic proofs use .99999~

[magilacudy]

X9=9 this will only be true if your some how asuming that X=1 not .99~. .99~ isn't areal number so it can go either way for practicle purposes use .99999.... for theoretic proofs use .99999~

How is 0.99~ not a 'real' number? It is computable and non-imaginary. BTW its good that the thread is back on track. :)

[Quackzilla]

Any infinite value is nonreal.
It's like the square root of -1.

0.999999~ = 0.999999~
It's just one of those "duh" things.
1 is a different number.

[magilacudy]

Any infinite value is nonreal.
It's like the square root of -1.

0.999999~ = 0.999999~
It's just one of those "duh" things.
1 is a different number.

I think we have a different definition of real numbers. My definition of a real number is a positive or negative non-complex i.e. doesn't involve the square root of -1. 0.99~ is nowhere near the jw-axis. I believe you are talking about rational numbers. According to these sites, infinite numbers are not irrational.

It is often erroneously assumed that mathematicians define "irrational number" in terms of decimal expansions, calling a number irrational if its decimal expansion neither repeats nor terminates. No mathematician takes that to be the definition, since the choice of base 10 would be arbitrary and since the standard definition is simpler and more well-motivated

However, there are numbers which are neither rational or irrational (for example, infinitesimal numbers are neither rational nor irrational

Infer what you want from that, that's enough math for me today.. whew.

[Pro]

Bump...?

[Mr. Anderson]

No! No BUMPING!

[Quackzilla]

.9~=.9~

1=1

1=/=.9~

[Don Chubo]

They don't equal.

[Rich]

10X = 9.999~
-1X = -1X (.999~)


What the hell did you do? Either that doesn't make mathematical sense, or I'm going crazy.

No matter; there are mathematical theorems that both prove and disprove that .99.... = 1 and .99.... != 1

It's a question you'll have to be happy not knowing the answer to, because we'll never know if it does, in fact, equal 1.

[godhatesjustyou]

Let X = .99999~

X = .9999~
10X = 9.999~
-1X = -1X (.999~)
9X = 9
X = 1


i think cause you didn't read it correctly.
you have x, which = .9999~
so
x = .999~
then you times both sides by 10
10x = 9.999~
then subtract 1x (which is .999~) from both sides
10x - 1x = 9.999~ - .999~
which equals
9x = 9
and then
x = 1

[Rich]

No, if that was the case, he's subtracting 1x from the left, and 1x(.999~) which is less than 1 until proven to be one; so therefor making the entire proof moot. By proving that .999~ is 1, you can't assume that .999~ is 1 until it's proven.

[chunk]

10X = 9.999~
-1X = -1X (.999~)


What the hell did you do? Either that doesn't make mathematical sense, or I'm going crazy.

No matter; there are mathematical theorems that both prove and disprove that .99.... = 1 and .99.... != 1

It's a question you'll have to be happy not knowing the answer to, because we'll never know if it does, in fact, equal 1.

Where is the proof that refutes their equality? I was under the impression that we (those of us that know) know that .999~=1 for a FACT.

[Storamin]

Limit as X->Infinity is 1. The whole point of a limit is that it never approaches it. Basic calculus teaches us this.

[eldad9]

.9~=.9~

1=1

1=/=.9~

What kind of "proof" is that?

It's equivalent to saying:

2+3 = 2+3
1+4 = 1+4
2+3 =/= 1+4

I will now repeat the correct answer
( http://www.mathforum.org/dr.math/faq/faq.0.9999.html )

Why does 0.9999... = 1 ?
This answer is adapted from an entry in the sci.math Frequently Asked Questions file, which is Copyright (c) 1994 Hans de Vreught (hdev@cp.tn.tudelft.nl).

The first thing to realize about the system of notation that we use (decimal notation) is that things like the number 357.9 really mean "3*100 + 5*10 + 7*1 + 9/10". So whenever you write a number in decimal notation and it has more than one digit, you're really implying a sum.

So in modern mathematics, the string of symbols 0.9999... = 1 is understood to mean "the infinite sum 9/10 + 9/100 + 9/1000 + ...". This in turn is shorthand for "the limit of the sequence of numbers

9/10,
9/10 + 9/100,
9/10 + 9/100 + 9/1000,
...."

One can show that this limit is 9/10 + 9/100 + 9/1000 ... using Analysis, and a proof really isn't all that hard (we all believe it intuitively anyway); a reference can be found in any of the Analysis texts referenced at the end of this message. Then all we have left to do is show that this sum really does equal 1:

Proof: 0.9999... = Sum 9/10^n
(n=1 -> Infinity)

= lim sum 9/10^n
(m -> Infinity) (n=1 -> m)

= lim .9(1-10^-(m+1))/(1-1/10)
(m -> Infinity)

= lim .9(1-10^-(m+1))/(9/10)
(m -> Infinity)

= .9/(9/10)

= 1


Not formal enough? In that case you need to go back to the construction of the number system. After you have constructed the reals (Cauchy sequences are well suited for this case, see [Shapiro75]), you can indeed verify that the preceding proof correctly shows

lim_(m --> oo) sum_(n = 1)^m (9)/(10^n) = 1

0.9999... = 1

Thus x = 0.9999...
10x = 9.9999...
10x - x = 9.9999... - 0.9999...
9x = 9
x = 1.


Another informal argument is to notice that all periodic numbers such as 0.9999... = 9/9 = 1 are equal to the digits in the period divided by as many nines as there are in the period. Applying the same argument to 0.46464646... gives us = 46/99.

References

R.V. Churchill and J.W. Brown. Complex Variables and Applications. 0.9999... = 1 ed., McGraw-Hill, 1990.

E. Hewitt and K. Stromberg. Real and Abstract Analysis. Springer-Verlag, Berlin, 1965.

W. Rudin. Principles of Mathematical Analysis. McGraw-Hill, 1976.

L. Shapiro. Introduction to Abstract Algebra. McGraw-Hill, 1975.

Bottom line:

Lock this thread already! next thing people will start asking about the third common word ending with "gry". Enough!

[Rich]

10X = 9.999~
-1X = -1X (.999~)


What the hell did you do? Either that doesn't make mathematical sense, or I'm going crazy.

No matter; there are mathematical theorems that both prove and disprove that .99.... = 1 and .99.... != 1

It's a question you'll have to be happy not knowing the answer to, because we'll never know if it does, in fact, equal 1.

Where is the proof that refutes their equality? I was under the impression that we (those of us that know) know that .999~=1 for a FACT.

It's not a fact. For every number you can conceive, you can always add a 9 in front of it. Saying .999~ is making the assumption that infinity actually exists; but as I said, you can ALWAYS add a 9 in front making the number. You can add a .9 in front of .999~, making the number .9infinity. As such, the number will always be less than 1 because you can always add .9 in front.
You will ALWAYS have a 1 there.

Since I suck at explaining this in words:

x = .99...
10x = 9.99....
9.00....1 != 9

Can always add an extra 9 to have the .1 show up. Hence; depends on whether or not you believe infinity exists or not.

[eldad9]

Hence; depends on whether or not you believe infinity exists or not.

By .999999... we mean an INFINITELY long series of nines. If your somehow don't believe that the concept of infinity exists (?????) (and again: ?????) you have no business even reading the rest of the problem.

Next we'll have people refusing to acknowledge the digit 6 exists on religious grounds.

For another example of mathematically-challenged freaks like the type you suggest exists, see:

http://www.snopes.com/religion/pi.htm

[Rich]

Hence; depends on whether or not you believe infinity exists or not.

By .999999... we mean an INFINITELY long series of nines. If your somehow don't believe that the concept of infinity exists (?????) (and again: ?????) you have no business even reading the rest of the problem.

Next we'll have people refusing to acknowledge the digit 6 exist on religious grounds.

For another example of mathematically-challenged freaks like the type you suggest exists, see:

http://www.snopes.com/religion/pi.htm

Mathematically-challenged? Because I can fuckin envision a number infinitely long + one more therefore not making it infinite? You're an idiot. No matter how infinitely long, there is always the possibility of one more. Get over yourself; you're not as smart as you think you are.

[eldad9]

Mathematically-challenged? Because I can shaq-fu envision a number infinitely long + one more therefore not making it infinite? You're an idiot. No matter how infinitely long, there is always the possibility of one more. Get over yourself; you're not as smart as you think you are.

You're not "envisioning" it correctly. Add one to a positive infinity, and it's still the same number. Maybe http://www.stormloader.com/ajy/hotel.html can clarify it.

The good news is that when you go to college and take more advanced math classes (calculus, etc) everything will start making sense to you.

In the meantime, I hope you'll forgive me for skipping the part of the post where I insult your intelligence, even though it is my turn.

[Rich]

Oh, you mean the intelligence insulting that you decided to start with your initial post?

I see infinity much different then you do; and as such, I see .999... as not equaling one.

Lets take 0 and .0000...1 for example. Do you believe that .0+infinity+1 = 0? I'd assume you do. But, alas, there IS always going to be a 1 at the end of that sequence thus not allowing it to =1. Just because there is no word to describe how small the number is, does not mean it equals one. Now take that infinitely smallest number imagineable that isn't =1 to win and subtract it from 1. You now have .99....; and you had to subtract something from 1 to get it. We can both agree on that, right? You just took 1, subtracted a number and came up with something different. If the logic was correct, wouldn't 1 - .0000...1 = 1 and not .99...?

Psst--this is more number theory than anything you can learn in a classroom. It can neither be proven for or against, since noone can ever accomplish infinity.

[Rich]

You're not "envisioning" it correctly. Add one to a positive infinity, and it's still the same number.


That's the thing. I don't think it IS the same number. If you added one, then the original number HAD to exist and had to end at some point since you added 1 to it.

PS--agree to stop insults from both sides. This really is an interesting as hell topic, and I'm sure we can both agree.

[thatstoobad]

It can neither be proven for or against, since noone can ever accomplish infinity.

if you say that you can't prove that you are right or wrong, could you do me a favor and let this topic die?

there's not much that can be said that hasn't been already.

[Rich]

No. it's interesting. Don't like it? Don't enter. Not that hard.

[video_gamer324]

Oh, you mean the intelligence insulting that you decided to start with your initial post?

I see infinity much different then you do; and as such, I see .999... as not equaling one.

Lets take 0 and .0000...1 for example. Do you believe that .0+infinity+1 = 0? I'd assume you do. But, alas, there IS always going to be a 1 at the end of that sequence thus not allowing it to =1. Just because there is no word to describe how small the number is, does not mean it equals one. Now take that infinitely smallest number imagineable that isn't =1 to win and subtract it from 1. You now have .99....; and you had to subtract something from 1 to get it. We can both agree on that, right? You just took 1, subtracted a number and came up with something different. If the logic was correct, wouldn't 1 - .0000...1 = 1 and not .99...?

Psst--this is more number theory than anything you can learn in a classroom. It can neither be proven for or against, since noone can ever accomplish infinity.

I'm not sure you fully understand the concept of infinity. Your value of .000...1 doesn't really exist because if you're looking for the smallest value greater than 0, you'll never get it. Even though you know that 1 has to go at the end, there is no end to infinity, and you can never pinpoint the exact location of where that 1 should go. Think in terms of scientific notation, where your value equals 1*10^x and x<=-2 - you will never find a place for that darn 1!

If that doesn't help, try this. 1/3*3 should equal 1, regardless of the base you use. However, only bases of multiples of 3 (i.e. base 9, base 12, etc.) can represent this perfectly in decimal form. Base 10 presents a slight problem, as 1/3=.333... and 3*.333...=.999..., but since 1/3*3 should equal 1, you could say that .999...=1.

[jeffreyjrose]

bump...

[video_gamer324]

---deleted---

[Rich]

I know that you can never pinpoint the place of the 1; but if infinity is in fact a number, you CAN place a number after it. If it's not a number, then, well, we're not making any sense. :p

No matter how many numbers you can amass, there is always room for another at the end, even if it's infinity. (Man, having an infinity symbol would make this so much easier)
.000infinity1 does exist, IMO. Like I said, it can't be proven to or to not exist, but IMO, it does. And as such, then there will always be an inequality. Think of it in reverse and you'll see where I'm coming from.

.1
.01
.001
.0001
Keep on going and you have the same number I'm trying to explain. You'll have an infinite amount of 0s ahead, but the 1 will always be at the end. Did that explain my thinking?


PS--your 1/3 problem is cool as hell and really gets me thinking, but I don't think anything is concrete evidence as to whether or not .99... = 1. I don't believe or disbelieve it. I'm just present a second side to the argument; as I can't prove either side correct. Who knows, maybe the answer to the age old question actually is: .999... does and does not equal 1.

[video_gamer324]

I know that you can never pinpoint the place of the 1; but if infinity is in fact a number, you CAN place a number after it. If it's not a number, then, well, we're not making any sense. :p

No matter how many numbers you can amass, there is always room for another at the end, even if it's infinity. (Man, having an infinity symbol would make this so much easier)
.000infinity1 does exist, IMO. Like I said, it can't be proven to or to not exist, but IMO, it does. And as such, then there will always be an inequality. Think of it in reverse and you'll see where I'm coming from.

.1
.01
.001
.0001
Keep on going and you have the same number I'm trying to explain. You'll have an infinite amount of 0s ahead, but the 1 will always be at the end. Did that explain my thinking?


PS--your 1/3 problem is cool as hell and really gets me thinking, but I don't think anything is concrete evidence as to whether or not .99... = 1. I don't believe or disbelieve it. I'm just present a second side to the argument; as I can't prove either side correct. Who knows, maybe the answer to the age old question actually is: .999... does and does not equal 1.

I think you're confusing yourself by classifying infinity as a number, not a concept. So really, you can't place a number after a concept, per se. Think of it this way: what's the greatest value less than 1? You know the answer should be .999..., but since that is only a concept and not a value, there is no correct answer.

[thatstoobad]

No. it's interesting. Don't like it? Don't enter. Not that hard.

the reason i said stop is because you are wrong, and there's not really much of an argument for you to make. you are saying that in your opinion infinity+1 is a valid statement, but it's not. there is nothing larger than infinity. you can say "x+1 > x" or maybe "n < n+6" but infinity+1 is still infinity.

you have the earlier argument that:
x = 0.9999...
10x = 9.9999...
10x - x = 9.9999... - 0.9999...
9x = 9
x = 1.
and you reply with "What the hell did you do? Either that doesn't make mathematical sense, or I'm going crazy. "

it's a valid statement, and it's got the same theory behind it as factorials. for instance, "(N+1)!/N! = (N+1)" because (N+1)! = (N+1)(N!), so you then cancel out the N! and you are left with (N+1). the reason for my bringing this up is because that it is the same thing as dividing by .9999~, since neither is a definitive number. so, if you look at it that way, .999~ has to equal 1, no matter what our better judgement may tell us.

a big problem here is that you keep saying "in my opinion", but in math, there isn't room for opinions. it's like going to a 15% off sale and picking up an item for $20, then you walk to the registers, the employee scans it, and tells you that it will cost you $17 (before they add tax to it), to which you reply "that doesn't sound right, i should get a larger discount." math is based on facts, not opinions.

[Rich]

But it's the concept OF a number.

con·cept (
n.
2. Something formed in the mind; a thought or notion. See Synonyms at idea.

Yup, something we can only form in our mind. But that doesn't mean that this isn't true:
.1
.01
.001
...
.0...1
equals
1 - .99...

Infinite numbers; only a concept with an answer that's only a concept. But that second concept is no less real than infinity or 1. Oh fuck, I just confused myself. Don't mind anything I just said.


Answer to the question? Nope, there's .00...1 difference between .999~ and 1.That's my take on things. I'm going to do some SERIOUS pondering about this tomarrow. My head hurts and I need sleep now.

1 - .99... = .00...1 makes just as little sense as the 1/3 problem, and quite frankly, it sucks knowing I'll never be able to explain it. :(

[Rich]

math is based on facts, not opinions.

And it's a FACT that infinity can always be expanded upon. It's the very definition of infinity. But no matter how much you expand upon infinite .9, it will still end in a 9 and thus, when subtracted from 1, will give you an answer of .infinity1
However, since no mathematician can properly solve equations with infinity, whether they'd like to or not, they can only give an opinion on the matter. There's no telling if infinity abides by the same number laws as every other number; which is where the opinions come in. It's YOUR opinion that infinity abides by all laws; it's mine that it doesn't.

[thatstoobad]

But it's the concept OF a number.

a concept is not the same as an opinion. inifinity is a concept. "green's a pretty color" is an opinion.

And it's a FACT that infinity can always be expanded upon.

you can expand infinity as far as you like, it's still infinity.

[eldad9]

You're not "envisioning" it correctly. Add one to a positive infinity, and it's still the same number.


That's the thing. I don't think it IS the same number. If you added one, then the original number HAD to exist and had to end at some point since you added 1 to it.


Adding a constant number to infinity doesn't change it. Them's the rules.

Do a search on Aleph-Null, if you will.

And/or
http://en.wikipedia.org/wiki/Infinity
more of Hilbert's hotel and an intuitive explanation
http://en.wikipedia.org/wiki/Hilbert's_paradox_of_the_Grand_Hotel

[Rich]

But it's the concept OF a number.

a concept is not the same as an opinion. inifinity is a concept. "green's a pretty color" is an opinion.

I edited my last post where I explained what is opinionated. Granted, chances are you won't agree, but quite frankly I'm done with this argument now.

[eldad9]

I think you're confusing yourself by classifying infinity as a number, not a concept. So really, you can't place a number after a concept, per se. Think of it this way: what's the greatest value less than 1? You know the answer should be .999..., but since that is only a concept and not a value, there is no correct answer.

No, the "greatest value less than 1" doesn't exist any more than "the largest prime number" does.

Look, suppose such a number existed. Let's mark it as X

since X<1,
X = X/2 + X/2 < X/2 + 1/2 < 1/2 + 1/2 = 1

So X/2 + 1/2 is larger than X and smaller than 1.

[Rich]

But it's the concept OF a number.

a concept is not the same as an opinion. inifinity is a concept. "green's a pretty color" is an opinion.

And it's a FACT that infinity can always be expanded upon.

you can expand infinity as far as you like, it's still infinity.

And you can make something infinitely less smaller, but that doesn't mean it will cease to exist. Which is the point I've been trying to make. By subtracting .99... from 1, you are making the difference INFINITELY less smaller, but alas, still existant.

PS--appreciate all of the explanations and links, eldad. It's nice to see someone not be an ass and still debate something. Odd thing on the internet. :)

[eldad9]

math is based on facts, not opinions.

However, since no mathematician can properly solve equations with infinity, whether they'd like to or not, they can only give an opinion on the matter. There's no telling if infinity abides by the same number laws as every other number; which is where the opinions come in. It's YOUR opinion that infinity abides by all laws; it's mine that it doesn't.

Wha? Where did you get this? What do they teach in American schools?

First meeting somebody who's convinced viruses can be written to target any computer, and now an infinity-denial.

(sorry if this sounded personal - it's not).

Please, don't accept the word of people who don't understand math. You're young, you're curious - learn about these things yourself.

[video_gamer324]

I think you're confusing yourself by classifying infinity as a number, not a concept. So really, you can't place a number after a concept, per se. Think of it this way: what's the greatest value less than 1? You know the answer should be .999..., but since that is only a concept and not a value, there is no correct answer.

No, the "greatest value less than 1" doesn't exist any more than "the largest prime number" does.

Look, suppose such a number existed. Let's mark it as X

since X<1,
X = X/2 + X/2 < X/2 + 1/2 < 1/2 + 1/2 = 1

So X/2 + 1/2 is larger than X and smaller than 1.

Yes, I realize that there is no greatest value less than 1, hence my earlier statement that "there is no correct answer," but perhaps I did not explain correctly. My apologies, and thanks for providing the correct mathematical support.

[Rich]

math is based on facts, not opinions.

However, since no mathematician can properly solve equations with infinity, whether they'd like to or not, they can only give an opinion on the matter. There's no telling if infinity abides by the same number laws as every other number; which is where the opinions come in. It's YOUR opinion that infinity abides by all laws; it's mine that it doesn't.

Wha? Where did you get this? What do they teach in American schools?

First meeting somebody who's convinced viruses can be written to target any computer, and now an infinity-denial.

(sorry if this sounded personal - it's not).

Please, don't accept the word of people who don't understand math. You're young, you're curious - learn about these things yourself.

How can ANYONE correctly assess the laws of infinity if they can't envision infinity?

By the logic presented to have the 2 numbers equal then my example of
.1, .01, .001 will eventually equal 0, correct? If it does, then what happens to that 1 at the end of the infinity? Does it just stop existing? It will always be there, correct? It will always be the difference of the 2 original numbers; thus making it equal to 0 since 1-1=0. But the 1 is there. How can anyone dispute that?

(I'm not accepting anyone word on any of this. This is just me trying to rationalize. I'm not even saying that .9999 doesn't equal 1; I'm just trying to find something that would prove it, but I'm just finding more things that disprove it. I realise half of this is coming out of my ass or making no sense; but I'm here trying to find answers, not really trying to argue, and if making a fool of myself is a byproduct of the quest for knowledge, then so be it.)

[eldad9]

Yes, I realize that there is no greatest value less than 1, hence my earlier statement that "there is no correct answer," but perhaps I did not explain correctly. My apologies, and thanks for providing the correct mathematical support.

Dood you were like there is no correct answer and then I was like there is a correct answer: no such number exists. But yes, we understand each other and vice versa.

I think RichD1's problem may be that he thinks he can get rid of the "..." at some point; he can't.

[Rich]

math is based on facts, not opinions.

However, since no mathematician can properly solve equations with infinity, whether they'd like to or not, they can only give an opinion on the matter. There's no telling if infinity abides by the same number laws as every other number; which is where the opinions come in. It's YOUR opinion that infinity abides by all laws; it's mine that it doesn't.

Wha? Where did you get this? What do they teach in American schools?

First meeting somebody who's convinced viruses can be written to target any computer, and now an infinity-denial.

(sorry if this sounded personal - it's not).

Please, don't accept the word of people who don't understand math. You're young, you're curious - learn about these things yourself.

Don't get me wrong; I'm NOT denying infinity's existance so much as I'm denying that by expanding upon infinity, you have to have something tangible to expand upon. 1+1+1+1 infitely, but when you get to an infinity plus 1s and add another +1, then the number you just added 1 to wasn't infinity. Oh hell, I don't even know what I'm talking about anymore; I just defined my logic with something that noone is even disagreeing with. I'll shut up now.

[Rich]

Yes, I realize that there is no greatest value less than 1, hence my earlier statement that "there is no correct answer," but perhaps I did not explain correctly. My apologies, and thanks for providing the correct mathematical support.

Dood you were like there is no correct answer and then I was like there is a correct answer: no such number exists. But yes, we understand each other and vice versa.

I think RichD1's problem may be that he thinks he can get rid of the "..." at some point; he can't.

No, I know the ... is infinite and such. But .0...1 exists, it's just not freaking palpable. As such, .999... and 1 are seperated by an untangible number, but one that exists. When I said it MIGHT not adhere to mathematically laws: there may quite possibly be a 4th dimension (time) involved in the equasion that can never be accounted for. The difference between the 2 is getting smaller for infinite amounts of time, but that doesn't take away from its existance. Should I shut up now? I'm not making sense.

[Rich]

I was just thinking of asymptotes. If .99...=1, then does that mean asymptotes are complete bullshit?

[The Successful Dropout]

so if a equals 11
and 319 equals zfx
then s8w definitely equals 5in4

right?

[scargums]

OK people, i just saw this thread and thought i would provide a DIFFERENT explanation as to why 1 is equal .999... that we talked about in my conceptual mathematics course at ohio state.

bascially one of the many ways to differentiate two numbers from one another is that you can find another number that lies between them. for instance .333... is equal to 1/3 because there are no possible numbers between them, but 1/3 and say 1/4 are not equal because you can find another number that lies between them. therefore, .999... is equal to 1 because of its infinite nature it is logically impossible to find a number that will differentiate 1 from .999..., therefore they are the same number. this also works with numbers like 4.999... = 5 and such.

in case your still confused with decimals, a number in between .50003 and .50004 would be .500032, as you can always extend the decimal place to find another number that would be in between two others, except obviously in an infinite case like .999... or .333... listed above

[eldad9]

By the logic presented to have the 2 numbers equal then my example of .1, .01, .001 will eventually equal 0, correct? If it does, then what happens to that 1 at the end of the infinity? Does it just stop existing? It will always be there, correct? It will always be the difference of the 2 original numbers; thus making it equal to 0 since 1-1=0. But the 1 is there. How can anyone dispute that?


I agree that dealing with infinites can be counter-intuitive - if you don't have the background for it you may not be able to grasp it (kinda like quantum physics). My problem is now to find an intuitive explanation to try and get you to understand it; if I'll fail in my task I'll try to confer with people who actually deal with math. Let's see...

In your example, you start with 1 and divide it by 10, an infinite amount of time. You can't say the last number in the series is or isn't zero, because there is no last number. What we mean by

lim (x-->infinity) 1/10^x

is the number 1/10^x approaches, as x itself approaches infinity (that is, grows and grows since you're essentialy counting the element you reached in the infinite series.

For every positive number you could think of, you'll eventually reach a number in the series which will be smaller (closer to 0), so the limit of this infimite series is zero. That's not to say there is an element in it that exactly equals zero, or that there is a last element.

Think of the "lim" function (or, as you called it, "...") as an additional function, like sine or log or whatever, that you just haven't learned about yet.

Makesense?

[Rich]

Calculus next year. Thank god. I honestly can't wait for college (such a short distance away. :( ) where I can actually take classes like scar said; conceptual math.

That's not to say there is an element in it that exactly equals zero, or that there is a last element.

That's just it, though; there is no element that exactly equals zero. If there was, then that means 1/10^x would eventually diminish itself into nothingness. (infinity and natural laws statement a whiles back) But if 1/10^x, as it approaches zero, keeps getting closer without ever actually reaching it, then that means 1-.99.. would approach zero but never hit it, thus always having SOME substance within itself, because if it ever hit 0, then that means 1/10^x as x approached 0 would have just diminshed itself into nothing, and therefore making .99... not true because 1-1 = 0. If only someone could get into my head and see what I'm thinking so they could properly explain it.

pssst, eldad, you rock. This is one of the best conversations I've been apart in in quite a while.

[eldad9]

Thanks, but I think most people who have taken calculus can explain it in some way - even though there are so many ways to explain it.

OK, think of it this way. On one hand, yes, the value of the number never reaches zero. But on the other hand, the index of the number you're looking it never reaches infinity. Those two nevers magically cancel each other out.

The "eventually" reaching zero doesn't make sense - because there is no eventuality, just an infinite series.

[rimsforsale]

this topic makes me so hot~~

whew... now i need a (_")3=~~~

[Wet Ninja]

...Who knows, maybe the answer to the age old question actually is: .999... does and does not equal 1.

Sounds like Schrödinger's cat...

Like you said, there's no way to know. So it does in a way parallel quantum mechanics.

[eldad9]

...Who knows, maybe the answer to the age old question actually is: .999... does and does not equal 1.

Sounds like Schrödinger's cat...

Like you said, there's no way to know. So it does in a way parallel quantum mechanics.

You're wrong. There is a way to know; I know; it is. The answer is that they're equal. If you don't understand that, you really don't understand what we mean by the "...".

The similarity to quantum physics is that it's very counter-intuitive; until your brain understands it, your mind will keep protesting, making understanding almost impossible. It is only when you allow yourself not to be bound by your intuition that you can actually begin to understand.

[lain21us]

Are you all stupid? All you uneducated morons talking about how cool this problem is, and how cool the guy who posted it must be to have come up with it. This is a BASIC concept is series. You learn it in any Discrete Math or second-semester Calculus class. .9999etc. is equal to one because it is the series (9/(10^(x+1))) from zero to infinity. This is equal to 9 tenths plus 9 hundreths, plus 9 thousandths, etc. It is INFINITELY close to one and thus converges to one. You cannot truly understand this problem if you haven't studied series. You cannot argue that the series never reaches one. It's not a numeric evaluation of an infinite sum. Because it gets infinitely close to one, it is equivalent to one, because there is no finite difference between the two. Leave math to the mathematicians. Thanks.

[lain21us]

Oh, and no, this has no similarity whatsoever to quantum physics.

[lain21us]

Damn it, I keep re-reading this post and getting more pissed. Whoever the hell said "there's no way to know" needs to get his uneducated, wishy-washy ass back to school. Of course there's a way to know. This isn't some f**king unresolvable paradox. This is cold hard mathematics, and these principles were discovered a hundred years before your little testicles dropped. Stop trying to sound cool and get to working on your algebra homework. Thank you.

[Rich]

I'm sorry, why do you post on these boards? I'm sure we'd be much better off without you.

[Wet Ninja]

That's what I get for posting at three in the morning before thinking through what I'm saying...

First of all, I haven't had Algebra homework, unless you count Abstract Algebra, in six years. I've probably had as much math as anyone on this board. It's hard not to when, in college, you double-major in computer science and physics, and come one class short of a math major.

I guess I just always separated the concept of convergence from the concept of equality. Whenever I studied infinite series, they were always said to "approach" some value, or "converge" to some value (unless they were divergent, of course); the term "equals" was never used. I guess that's where the ambiguity comes in for me. I always thought that when a series converged to a particular value, then it wasn't quite equal to that value, but was inifinitely close to it (as you said, "a numeric evaluation of an infinite sum"). I thought that it was still possible to insert an infinitely small, yet nonzero term between the two. But, if, as you say, "there is no finite difference between the two," then I'll believe that they are equal. The distinction was never made clear when I studied infinite series, and I never questioned it. For the purposes for which I used infinite series, speaking vaguely about convergence rather than explicitly stating equality was sufficient. I suppose it turns out that they are the same.

[scargums]

you guys seem to have skipped over my post, as it is clearly explained in a simple way that has not been used before in this thread, but you all seem hellbent on thinking it requires caculus or quantum physics or something else insanely complicated. ITS EQUAL BECAUSE THERE IS NO WAY TO DIFFERENTIATE THE TWO. thats it!! THERE IS NO NUMBER IN BETWEEN .999... and 1, THEREFORE THEY ARE EQUAL. a slightly more detailed (but still simple) explantion is listed above in my earlier post on this page.

This exact problem was discussed in my conceptual mathematics course, and THIS IS THE SOLUTION, plain and simple. if you choose to continue to ignore my post and whine about how to find the answer for another 20 pages be my guest, but if you want to know the actual answer to the problem, just read it!

[chunk]

How can ANYONE correctly assess the laws of infinity if they can't envision infinity?

By the logic presented to have the 2 numbers equal then my example of
.1, .01, .001 will eventually equal 0, correct? If it does, then what happens to that 1 at the end of the infinity? Does it just stop existing? It will always be there, correct? It will always be the difference of the 2 original numbers; thus making it equal to 0 since 1-1=0. But the 1 is there. How can anyone dispute that?

You prove it yourself because you contradict yourself.

By definition .000.... doesn't have an end. That is the whole idea. So when you say "at the end of the infinity" you are contradicting yourself.

By definition .0000......1 means "a decimal point followed by a never ending number of zeros with a 1 at the end"

It can't be both neverending and have something at the end. Clearly this makes sense to you. Neverending and having an end are opposites. So your "disproof" is absolute nonsense.

By your argument, if .999.... and 1 are not equal then .000....1 would be the difference. However, .000....1 cannot exist by definition (as I explained above). Therefore, .9999.... and 1 must be equal.

This is the whole idea of mathematics. It is not some metaphysical mystery that might be different in a parallel universe. There are a handful of simple logical statements and everything else unquestionably follows from those ideas (one of those ideas being that you can't contradict yourself......you can't say "at the end of the something that never ends"). If you agree that something can't be both true and false at the same time then, by definition, you agree that .999.....=1.

[Quackzilla]

Let X = .99999~

X = .9999~
10X = 9.999~
-1X = -1X (.999~)
9X = 9
X = 1


i think cause you didn't read it correctly.
you have x, which = .9999~
so
x = .999~
then you times both sides by 10
10x = 9.999~
then subtract 1x (which is .999~) from both sides
10x - 1x = 9.999~ - .999~
which equals
9x = 9
and then
x = 1

You can not add, subtrct, multiply, or divide with an infinite number.

[thatstoobad]

You can not add, subtrct, multiply, or divide with an infinite number.

.999~ is not an infinite number, in the sense that it could be any number like infinity could. dividing .999~ by .999~ will always result in 1, because even though the .999~ goes on forever, it will always be matched by the .999~ you are dividing into it, thus resulting in 1. this could be worded poorly, so here is an example with a different number:

pi/pi = 1

unless you want to argue that.

[x0thedeadzone0x]

~ = an estimate of an equal, not infinity. the infinite of a number is determined by a line over the number in a decimal point
_
.99 for example (if that came out right)

but don't take my word for it. clearly this is an advanced problem and i don't want to get in the way of the line of fire with all these mathmeticians debating over this.

[thatstoobad]

~ = an estimate of an equal, not infinity. the infinite of a number is determined by a line over the number in a decimal point
_
.99 for example (if that came out right)

but don't take my word for it. clearly this is an advanced problem and i don't want to get in the way of the line of fire with all these mathmeticians debating over this.

the reason ".999~" is being used is because it's far easier than:
_
.999

because you'd have to start a new line every time you'd want to write it if you were doing that, and that would be annoying.

you'd need two ~ on top of each other for an estimate of an equal.

[Rich]

How can ANYONE correctly assess the laws of infinity if they can't envision infinity?

By the logic presented to have the 2 numbers equal then my example of
.1, .01, .001 will eventually equal 0, correct? If it does, then what happens to that 1 at the end of the infinity? Does it just stop existing? It will always be there, correct? It will always be the difference of the 2 original numbers; thus making it equal to 0 since 1-1=0. But the 1 is there. How can anyone dispute that?

You prove it yourself because you contradict yourself.

By definition .000.... doesn't have an end. That is the whole idea. So when you say "at the end of the infinity" you are contradicting yourself.

By definition .0000......1 means "a decimal point followed by a never ending number of zeros with a 1 at the end"

It can't be both neverending and have something at the end. Clearly this makes sense to you. Neverending and having an end are opposites. So your "disproof" is absolute nonsense.

By your argument, if .999.... and 1 are not equal then .000....1 would be the difference. However, .000....1 cannot exist by definition (as I explained above). Therefore, .9999.... and 1 must be equal.

This is the whole idea of mathematics. It is not some metaphysical mystery that might be different in a parallel universe. There are a handful of simple logical statements and everything else unquestionably follows from those ideas (one of those ideas being that you can't contradict yourself......you can't say "at the end of the something that never ends"). If you agree that something can't be both true and false at the same time then, by definition, you agree that .999.....=1.

So you're saying you can't keep going .1 .01 .001 infinitely, but can do the same thing if you start with a .0, .00, .000?

[chunk]

So you're saying you can't keep going .1 .01 .001 infinitely, but can do the same thing if you start with a .0, .00, .000?

You keep throwing around this word infinity. Try defining exactly what you mean. The answer to the problem will follow clearly from the definitions. There are two definitions that you might want to use (at least only two that I will address).

If you say that "going .1 .01 .001 infinitely" means that you keep repeating that process forever then you will obviously never have a completed value because you never stop the process your using to construct it. In other words, you have the completed value when you are finished, but if you keep repeating forever then you are never finished. So the only value you can really talk about is the value that you are approaching. Clearly the number you are approaching is zero because each time you add another zero to the left you get closer to zero. It doesn't make sense to talk about the completed values of either .000...1 or .000... because by this definition of infinity there are no completed values (you are never finished making them). Note the fact that these two numbers don't have a final value because of the definition of infinity that we used (its not that we just can't figure it out, it directly follows from our definition of infinity). The only thing that we can compare is what each number is approaching and they are both approaching the same value (zero). So you can either define the values that you mean by .000...1 and .000... as the values that each sequence is approaching or you have to say that they don't really have values at all because they are never completed (in which case .000...1 and .000... are no longer defined as numbers).

The other way to definine an infinite sequence is to simply say that the sequence doesn't have an end. This is just like I described before. If the sequence doesn't end then you can't have something at the end. It doesn't matter if you put what you want at the end first and then put your neverending sequence to the left. For example, if you put .000... (never ending sequence of zeros) to the left of a 1 that doesn't mean that you have a 1 at the end. Sure you can write it like this ".000...1", but the 1 can't be at the end (by definition). Maybe you can say its in another universe or something, but wherever it is it can't be at the end because .000... has no end. If you say it has an end then it isn't .000... because .000... is defined as a sequence of zeros with no end. You can't say that there is a zero at the end either because there is no end! Therefore (by this definition of infinity), .000...1 is a contradiction. Just like if I say that I'm both 53 and 21 years old. See it is possible to express a contradiction, but that doesn't mean that what you are expressing is possible. I can say I'm both 53 and 21 years old but such a case cannot exist because if I were 53 then I wouldn't be 21 (by definition of 53 years and 21 years).

These two definitions might actually be the same. I'm not sure (any mathematicians in the house? I'm only an engineer). If you have some other definition of infinity then give it and we can go from there. I think that you will find that any agreeable definition for infinity will give you the same result.