.9999~ = 1. Prove me wrong

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SS4Brolly

SS4Brolly

CAGiversary!
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.
 
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?
 
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?
 
Here's some collaboration

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.
 
[quote name='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?[/quote]

See if this helps:

x=.999~
10x=10(.999~)=9.999~
10x-1x=9.999~-(.999~)
9x=9
x=1
 
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.
 
[quote name='video_gamer324'][quote name='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?[/quote]

See if this helps:

x=.999~
10x=10(.999~)=9.999~
10x-1x=9.999~-(.999~)
9x=9
x=1[/quote]

now that makes sense!

..wow, that is really wierd..
 
doesn't that whole thing depend on significant figures? if you do proper math with sig fig it does not equal out.
 
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.
 
[quote name='video_gamer324'][quote name='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?[/quote]

See if this helps:

x=.999~
10x=10(.999~)=9.999~
10x-1x=9.999~-(.999~)
9x=9
x=1[/quote]

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.
 
^^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
 
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. "
 
[quote name='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.[/quote]

Order of Operations:
Parenthesis
Expontents
Multiplication
Division
Addition
Subtraction

PEMDAS is actually a fairly decent mnemonic device for remembering that.
 
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.
 
-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
 
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.
 
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
 
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.
 
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?
 
[quote name='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?[/quote]

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.
 
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? :(
 
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.
 
[quote name='Mr. Anderson']The pain inside my brain is at scorching right now. Please, somebody lock this before my head explodes.[/quote]

I like your sig, but it's a little too big. It's also stretched out.
 
[quote name='Scrubking'][quote name='Mr. Anderson']The pain inside my brain is at scorching right now. Please, somebody lock this before my head explodes.[/quote]

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

I'll try to see what I can do.
 
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
 
[quote name='JSweeney'][quote name='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?[/quote]

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.[/quote]

Prove that you're not a figment of my imagination.
 
[quote name='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?

[/quote]

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.
 
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...
 
[quote name='GameDude'][quote name='JSweeney'][quote name='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?[/quote]

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.[/quote]

Prove that you're not a figment of my imagination.[/quote]

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?
 
[quote name='JSweeney'][quote name='GameDude'][quote name='JSweeney'][quote name='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?[/quote]

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.[/quote]

Prove that you're not a figment of my imagination.[/quote]

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?[/quote]

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.
 
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!
 
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.
 
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.
 
[quote name='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.[/quote]

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.
 
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