.9999~ = 1. Prove me wrong
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lain21us
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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.
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.
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
CAGiversary!
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!
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!
[quote name='RichD1']
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?[/quote]
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.
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?[/quote]
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
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[quote name='godhatesjustyou'][quote name='SS4Brolly']Let X = .99999~
X = .9999~
10X = 9.999~
-1X = -1X (.999~)
9X = 9
X = 1
[/quote]
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[/quote]
You can not add, subtrct, multiply, or divide with an infinite number.
X = .9999~
10X = 9.999~
-1X = -1X (.999~)
9X = 9
X = 1
[/quote]
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[/quote]
You can not add, subtrct, multiply, or divide with an infinite number.
thatstoobad
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[quote name='Quackzilla']You can not add, subtrct, multiply, or divide with an infinite number.[/quote]
.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.
.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
CAGiversary!
~ = 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.
_
.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
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[quote name='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.[/quote]
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.
_
.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.[/quote]
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.
[quote name='chunk'][quote name='RichD1']
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?[/quote]
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.[/quote]
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?
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?[/quote]
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.[/quote]
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?
[quote name='RichD1']
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?[/quote]
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.
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?[/quote]
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.
SKIP TO BOTTOM FOR SUMMARY I view neither way yet, although seem to be biased towards it not equaling.
About the whole reality thing...
Reality is what we take to be true. What we take to be true is what we believe. What we believe is based upon our perceptions. What we perceive depends upon what we look for. What we look for depends upon what we think. What we think depends upon what we perceive. What we perceive determines what we believe. What we believe determines what we take to be true. what we take to be true is our reality.
There you go for the philosopher part...
And the whole basics of Calculus is that as .99~ approaches infinity that the value is considered to be 1. But I have some arguments for both sides.
First infinity is an idea, it is a "belief" if you will. It was created in order to show that numbers do not stop after a decimal point. Every number goes on for an infinite amount of numbers. 1/3 = .333333~. 3/3= 1.000000~
Next all non terminating fractions cannot be expressed with a calculator, nor by hand, the whole premise behind this is it is non terminating so we say it does not stop until it reaches infinity.
Infinity is not a value, it is a limit. It is like finding the Correlation Coefficient, the limits are -1 and 1. It is impossible to surpass that limit, unlike a value which is passable.
A value "[SIZE=-1]a numerical quantity measured or assigned or computed" or "[/SIZE][SIZE=-1]fix or determine the value of". 1/3 and 2/3 are not values in anyway, all that the fraction means is that 1/3 is .333 repeating infinitively. It is a limit, 1/3 says that .3333~ can never surpass its limit, which is .3333~ surpass infinite amounts of 3's, so it is a limit. Same with 2/3.
Now 3/3 is a value. It can be defined, it can be calculated or measured. 3/3 is equal to 1.
Next I was told of an argument about time, it was something like this. "Obviously infinity stops somewhere, somehow the infinite moments in time meet in order to make another moment." If you ever hear this argument smack the person in the head. Time is a creation by man, we do not control the passing of it but we control the intervals and the only reason the "infinite" amount of moments in between equals another is just ignorant. The next moment in time is a limit.
Also the amount of numbers between 1-2 and 1-4 are all the same if you think infinitivly.
OK I just babbled on and on, and I am not no mathematician, hardly but these are my views on this subject.
Overview: Inifinity is a belief of a limitless limit. .3333~ unsimplified = .3333 MULTIPLIED by infinity. Since it is multiplied by a limit, it equals a limit. 3/3 = 1 which is a defined value. If infinity were defined and could be reached, how come the numbers between 1-2 and 1-4 are the same?
I'm insane and ignorant.
[/SIZE]
About the whole reality thing...
Reality is what we take to be true. What we take to be true is what we believe. What we believe is based upon our perceptions. What we perceive depends upon what we look for. What we look for depends upon what we think. What we think depends upon what we perceive. What we perceive determines what we believe. What we believe determines what we take to be true. what we take to be true is our reality.
There you go for the philosopher part...
And the whole basics of Calculus is that as .99~ approaches infinity that the value is considered to be 1. But I have some arguments for both sides.
First infinity is an idea, it is a "belief" if you will. It was created in order to show that numbers do not stop after a decimal point. Every number goes on for an infinite amount of numbers. 1/3 = .333333~. 3/3= 1.000000~
Next all non terminating fractions cannot be expressed with a calculator, nor by hand, the whole premise behind this is it is non terminating so we say it does not stop until it reaches infinity.
Infinity is not a value, it is a limit. It is like finding the Correlation Coefficient, the limits are -1 and 1. It is impossible to surpass that limit, unlike a value which is passable.
A value "[SIZE=-1]a numerical quantity measured or assigned or computed" or "[/SIZE][SIZE=-1]fix or determine the value of". 1/3 and 2/3 are not values in anyway, all that the fraction means is that 1/3 is .333 repeating infinitively. It is a limit, 1/3 says that .3333~ can never surpass its limit, which is .3333~ surpass infinite amounts of 3's, so it is a limit. Same with 2/3.
Now 3/3 is a value. It can be defined, it can be calculated or measured. 3/3 is equal to 1.
Next I was told of an argument about time, it was something like this. "Obviously infinity stops somewhere, somehow the infinite moments in time meet in order to make another moment." If you ever hear this argument smack the person in the head. Time is a creation by man, we do not control the passing of it but we control the intervals and the only reason the "infinite" amount of moments in between equals another is just ignorant. The next moment in time is a limit.
Also the amount of numbers between 1-2 and 1-4 are all the same if you think infinitivly.
OK I just babbled on and on, and I am not no mathematician, hardly but these are my views on this subject.
Overview: Inifinity is a belief of a limitless limit. .3333~ unsimplified = .3333 MULTIPLIED by infinity. Since it is multiplied by a limit, it equals a limit. 3/3 = 1 which is a defined value. If infinity were defined and could be reached, how come the numbers between 1-2 and 1-4 are the same?
I'm insane and ignorant.
[/SIZE]
SKIP TO BOTTOM FOR SUMMARY I view neither way yet, although seem to be biased towards it not equaling.
About the whole reality thing...
Reality is what we take to be true. What we take to be true is what we believe. What we believe is based upon our perceptions. What we perceive depends upon what we look for. What we look for depends upon what we think. What we think depends upon what we perceive. What we perceive determines what we believe. What we believe determines what we take to be true. what we take to be true is our reality.
There you go for the philosopher part...
And the whole basics of Calculus is that as .99~ approaches infinity that the value is considered to be 1. But I have some arguments for both sides.
First infinity is an idea, it is a "belief" if you will. It was created in order to show that numbers do not stop after a decimal point. Every number goes on for an infinite amount of numbers. 1/3 = .333333~. 3/3= 1.000000~
Next all non terminating fractions cannot be expressed with a calculator, nor by hand, the whole premise behind this is it is non terminating so we say it does not stop until it reaches infinity.
Infinity is not a value, it is a limit. It is like finding the Correlation Coefficient, the limits are -1 and 1. It is impossible to surpass that limit, unlike a value which is passable.
A value "a numerical quantity measured or assigned or computed" or "fix or determine the value of". 1/3 and 2/3 are not values in anyway, all that the fraction means is that 1/3 is .333 repeating infinitively. It is a limit, 1/3 says that .3333~ can never surpass its limit, which is .3333~ surpass infinite amounts of 3's, so it is a limit. Same with 2/3.
Now 3/3 is a value. It can be defined, it can be calculated or measured. 3/3 is equal to 1.
Next I was told of an argument about time, it was something like this. "Obviously infinity stops somewhere, somehow the infinite moments in time meet in order to make another moment." If you ever hear this argument smack the person in the head. Time is a creation by man, we do not control the passing of it but we control the intervals and the only reason the "infinite" amount of moments in between equals another is just ignorant. The next moment in time is a limit.
Also the amount of numbers between 1-2 and 1-4 are all the same if you think infinitivly.
OK I just babbled on and on, and I am not no mathematician, hardly but these are my views on this subject.
Overview: Inifinity is a belief of a limitless limit. .3333~ unsimplified = .3333 MULTIPLIED by infinity. Since it is multiplied by a limit, it equals a limit. 3/3 = 1 which is a defined value. If infinity were defined and could be reached, how come the numbers between 1-2 and 1-4 are the same?
I'm insane and ignorant.
About the whole reality thing...
Reality is what we take to be true. What we take to be true is what we believe. What we believe is based upon our perceptions. What we perceive depends upon what we look for. What we look for depends upon what we think. What we think depends upon what we perceive. What we perceive determines what we believe. What we believe determines what we take to be true. what we take to be true is our reality.
There you go for the philosopher part...
And the whole basics of Calculus is that as .99~ approaches infinity that the value is considered to be 1. But I have some arguments for both sides.
First infinity is an idea, it is a "belief" if you will. It was created in order to show that numbers do not stop after a decimal point. Every number goes on for an infinite amount of numbers. 1/3 = .333333~. 3/3= 1.000000~
Next all non terminating fractions cannot be expressed with a calculator, nor by hand, the whole premise behind this is it is non terminating so we say it does not stop until it reaches infinity.
Infinity is not a value, it is a limit. It is like finding the Correlation Coefficient, the limits are -1 and 1. It is impossible to surpass that limit, unlike a value which is passable.
A value "a numerical quantity measured or assigned or computed" or "fix or determine the value of". 1/3 and 2/3 are not values in anyway, all that the fraction means is that 1/3 is .333 repeating infinitively. It is a limit, 1/3 says that .3333~ can never surpass its limit, which is .3333~ surpass infinite amounts of 3's, so it is a limit. Same with 2/3.
Now 3/3 is a value. It can be defined, it can be calculated or measured. 3/3 is equal to 1.
Next I was told of an argument about time, it was something like this. "Obviously infinity stops somewhere, somehow the infinite moments in time meet in order to make another moment." If you ever hear this argument smack the person in the head. Time is a creation by man, we do not control the passing of it but we control the intervals and the only reason the "infinite" amount of moments in between equals another is just ignorant. The next moment in time is a limit.
Also the amount of numbers between 1-2 and 1-4 are all the same if you think infinitivly.
OK I just babbled on and on, and I am not no mathematician, hardly but these are my views on this subject.
Overview: Inifinity is a belief of a limitless limit. .3333~ unsimplified = .3333 MULTIPLIED by infinity. Since it is multiplied by a limit, it equals a limit. 3/3 = 1 which is a defined value. If infinity were defined and could be reached, how come the numbers between 1-2 and 1-4 are the same?
I'm insane and ignorant.
crushtopher
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.9999~ = 1
is not true for the simple fact that there are 6 symbols on the left side of the =, and one on the right. duh
is not true for the simple fact that there are 6 symbols on the left side of the =, and one on the right. duh
- Status
bread's done