EvilZone
Encyclopedia Galactica => Science => : Daemon February 09, 2013, 10:58:32 PM
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This is a quote from a fiction book I read, the logic seems sound but im horrible at math so i thought I'd post it here. I'd like to see someone either A. Prove or disprove this through an actual equation (if possible) or B. tell me im a crackpot who needs to stop reading books 8)
“You can divide infinity an infinite number of times, and the resulting pieces will still be infinitely large. But if you divide a non-infinite number an infinite number of times the resulting pieces are non-infinitely small. Since they are non-infinitely small, but there are an infinite number of them, if you add them back together, their sum is infinite. This implies any number is, in fact, infinite.”
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You can't divide a number an infinite number of times... just as you can't divide by 0.
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There's no way this could be proven, I'm sure there'll be an argument on how to properly go about disproving this.. maybe I'll give it a shot this time.
It's a given that
∞/∞ = ∞
But if you took a real number, say 100, divided by infinity, like so:
100/∞
you would have to divide 100 by every succeeding number, giving a smaller output, like so:
100/100 = 1
100/101 = .99009900 (repeating)
100/102 = .9803.......
etc.
The result is an infinite number of smaller numbers. To add them all back together would mean adding the quotient of an infinite number of equations where a constant number is divided by a variable number exceeding the constant number's value. Adding these together would continue to grow, essentially = ∞.
However, you deal with the constant number multiple times, not just once, so adding the resulting answer every time isn't correlated to the constant number, but rather the variable number. This doesn't prove that any number is infinite, but this does prove that any number divided by infinity always equals infinity
100/∞ = ∞
101/∞ = ∞
Another thing wrong about that statement, is "the resulting pieces are non-infinitely small". Numbers can theoretically keep getting smaller in the same way that they can get larger. This fact doesn't change much but hopefully I effectively disproved this, I'm not very good at math though..
You can't divide a number an infinite number of times... just as you can't divide by 0.
We just can't grasp the concept of dividing by 0, I'm sure it can be done. Think of when the concept of 0 was nonexistant, I'm sure at some point in time we will realize how to divide by 0 and then it'll become common law.
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We just can't grasp the concept of dividing by 0, I'm sure it can be done. Think of when the concept of 0 was nonexistant, I'm sure at some point in time we will realize how to divide by 0 and then it'll become common law.
Its not that we can't grasp the concept of dividing by 0, its the fact that it's impossible to divide by 0. 0 is the null operator in maths and so you can't divide by it. The rest of your post is pretty good :D
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Wow, silenthunder's post actually kind of proved it. Not a full on equation...but still.
“You can divide infinity an infinite number of times, and the resulting pieces will still be infinitely large.
It's a given that
∞/∞ = ∞
But if you divide a non-infinite number an infinite number of times the resulting pieces are non-infinitely small.
But if you took a real number, say 100, divided by infinity, like so:
100/∞
you would have to divide 100 by every succeeding number, giving a smaller output, like so:
100/100 = 1
100/101 = .99009900 (repeating)
100/102 = .9803.......
etc.
Since they are non-infinitely small, but there are an infinite number of them, if you add them back together, their sum is infinite. This implies any number is, in fact, infinite.”
The result is an infinite number of smaller numbers. To add them all back together would mean adding the quotient of an infinite number of equations where a constant number is divided by a variable number exceeding the constant number's value. Adding these together would continue to grow, essentially = ∞.
Another thing wrong about that statement, is "the resulting pieces are non-infinitely small". Numbers can theoretically keep getting smaller in the same way that they can get larger. This fact doesn't change much but hopefully I effectively disproved this, I'm not very good at math though..
It's impossible for numbers to get infinitely smaller, because eventually you will reach zero. While you can continue finding even smaller numbers, there is a definite point where they end, and that's 0. Therefore, they are non-infinitely small. Just saying
Well written though, and thank you :)
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There is one simple flaw...
if you divide a non infinite number, infinite number of times by infinity...
what you're doing is
A/B + A/D..... and so on....
what gave you the right to divide a number by different numbers and add the quotients and claim that the result is the number itself.?
it's like saying..
6/2 + 6/3 + 6/4 ..... = 6....
that's not true... The statement is wrong...
the divided pieces.. (Quotients)... Cannot be added together to gain the number back...
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There is one simple flaw...
if you divide a non infinite number, infinite number of times by infinity...
what you're doing is
A/B + A/D..... and so on....
what gave you the right to divide a number by different numbers and add the quotients and claim that the result is the number itself.?
it's like saying..
6/2 + 6/3 + 6/4 ..... = 6....
that's not true... The statement is wrong...
the divided pieces.. (Quotients)... Cannot be added together to gain the number back...
F if i know man, i clearly stated im not too great with math. And i read this in a book lol
Thanks for that explanation then
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It's impossible for numbers to get infinitely smaller, because eventually you will reach zero. While you can continue finding even smaller numbers, there is a definite point where they end, and that's 0. Therefore, they are non-infinitely small. Just saying
Well written though, and thank you :)
Think of the order of numbers for a second. You have the one's digit, the ten's digit 100's digits, 1000's digits, 10000's digits, and so on. This is where the idea of infinity came from. when you go the opposite direction, you start in the tenths. Then you move to the hundreths, thousanths, ten-thousanths, one-hundred-thousanths, and so on. Meaning that no matter how small the number gets, it is still not zero.
There is one simple flaw...
if you divide a non infinite number, infinite number of times by infinity...
what you're doing is
A/B + A/D..... and so on....
what gave you the right to divide a number by different numbers and add the quotients and claim that the result is the number itself.?
it's like saying..
6/2 + 6/3 + 6/4 ..... = 6....
that's not true... The statement is wrong...
the divided pieces.. (Quotients)... Cannot be added together to gain the number back...
While what your saying is true, the fact remains that the number is still growing at a gradually slower, but still infinite rate. It is virtually true that the number will never be regained, however if we had a computer infinitely more powerful than the one computer pi, it would eventually reach and even surpass the original number, although it would take so many years that Earth probably wouldn't even be around by then (hence the "virtually" impossible). But that still doesn't prove that the original real number equals infinity, because it is used more than once, in in an infinite number of equations, in order to achieve infinity.
The closest you could ever get to 100 = ∞ would be something similar to this:
100 = (100/100) + (100/101) + (100/102) + (100/103) (100/.... = ∞
However, if you were to apply my theory that EVENTUALLY the original number (100) would be surpassed, it is no longer = ∞, at that point 100>∞.
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Think of the order of numbers for a second. You have the one's digit, the ten's digit 100's digits, 1000's digits, 10000's digits, and so on. This is where the idea of infinity came from. when you go the opposite direction, you start in the tenths. Then you move to the hundreths, thousanths, ten-thousanths, one-hundred-thousanths, and so on. Meaning that no matter how small the number gets, it is still not zero.
While what your saying is true, the fact remains that the number is still growing at a gradually slower, but still infinite rate. It is virtually true that the number will never be regained, however if we had a computer infinitely more powerful than the one computer pi, it would eventually reach and even surpass the original number, although it would take so many years that Earth probably wouldn't even be around by then (hence the "virtually" impossible). But that still doesn't prove that the original real number equals infinity, because it is used more than once, in in an infinite number of equations, in order to achieve infinity.
The closest you could ever get to 100 = ∞ would be something similar to this:
100 = (100/100) + (100/101) + (100/102) + (100/103) (100/.... = ∞
However, if you were to apply my theory that EVENTUALLY the original number (100) would be surpassed, it is no longer = ∞, at that point 100>∞.
um, no...
look... If you take the infinity form...
100/ ∞ + 100/ ∞...... And so on ....
This is a summation.....
Now, take 100 common...
Which yields...
100( 1/ ∞................ Infinite time)...
Now, 1/infinity is zero...
if you take it this way then you get zero...
But if you say that you add the quotients of 100 by infinity an infinite number of times..
You'll get 100 back...
the thing is that ( ∞/∞) can't be DETERMINED...
you can argue it as 1 or zero... And hence you get 100 or 0 as your answer...
the problem is that infinite cannot be quantized....
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um, no...
look... If you take the infinity form...
100/ ∞ + 100/ ∞...... And so on ....
This is a summation.....
Now, take 100 common...
Which yields...
100( 1/ ∞................ Infinite time)...
Now, 1/infinity is zero...
if you take it this way then you get zero...
But if you say that you add the quotients of 100 by infinity an infinite number of times..
You'll get 100 back...
the thing is that ( ∞/∞) can't be DETERMINED...
you can argue it as 1 or zero... And hence you get 100 or 0 as your answer...
the problem is that infinite cannot be quantized....
Yeah someone else mentioned summations to me too and then proceeded to same the same thing about how ∞ can't be determined and stuff, but then he realized that we're arguing the same point that the OP's equation isn't true and is invalid. I did say there would be an argument on HOW we disproved it, and that's exactly what's going on. I'm not good at math at all so I'm out of contributions to this, I don't even know what a summation is lol.
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The result is an infinite number of smaller numbers. To add them all back together would mean adding the quotient of an infinite number of equations where a constant number is divided by a variable number exceeding the constant number's value. Adding these together would continue to grow, essentially = ∞.
No, it will grow infinitely, but converging the original number (limit: https://en.wikipedia.org/wiki/Limit_%28mathematics%29). That's where your flaw in thinking is. Infinite grow doesn't mean the value will be infinite.
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This is true because there are two infinities. A. the infinite number of decimal places between 1-2, for example 1.85749575847694 and so on. Then there is the infinite amount of integers which will never end so you can divide infinity by infinity an infinite amount of times.
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Kmon guys, infinity is not a number. Once you make infinity a number, you make it finite.
What does it mean to divide a number by infinity? It's impossible since infinity is not a number. One might say, what about dividing a number infinite amount of times. Dividing infinitely by what? Say divide by a number x. Well then this dividing process will never, end will it, since you divide the number infinitely.
The flaw is in the problem, thus all the solutions that accept/ignore/don't notice the flaw are flawed themselves.
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Kmon guys, infinity is not a number. Once you make infinity a number, you make it finite.
What does it mean to divide a number by infinity? It's impossible since infinity is not a number. One might say, what about dividing a number infinite amount of times. Dividing infinitely by what? Say divide by a number x. Well then this dividing process will never, end will it, since you divide the number infinitely.
The flaw is in the problem, thus all the solutions that accept/ignore/don't notice the flaw are flawed themselves.
Well it is dividing a number an infinite amount of times, but not by one specific number. I am theorizing that to divide a number by infinity, you would have to divide it by every existing number, given that there's an infinite number of existing numbers.
100/1
100/2
100/3
100/4
etc.
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guys u knew that pi is a number that combines every single digit ? it means it could contain the date of your birthday your bank account number your telephone number because it combines all numbers in all ways its crazy :P
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Kmon guys, infinity is not a number. Once you make infinity a number, you make it finite.
What does it mean to divide a number by infinity? It's impossible since infinity is not a number. One might say, what about dividing a number infinite amount of times. Dividing infinitely by what? Say divide by a number x. Well then this dividing process will never, end will it, since you divide the number infinitely.
The flaw is in the problem, thus all the solutions that accept/ignore/don't notice the flaw are flawed themselves.
s3my0n actually has the most correct point.
First of all you cannot operate with infinity. It is not a number (although in mathematics for ease of use we accept is as one sometimes) but it is a concept denoted by a symbol.
Infinity is actually originating from limit theory. The problem was that there was no way to represent how an exponential function (as an example) behaves when the exponent is a very very large number.
Basically what is calculated is the tendency of the function. In the case of a normal exponential, the function converges to infinity when the exponent tends to infinity. This is the correct way of formulating from a mathematical point of view - and you'll notice that I never said "equals infinity" or the likes because that is illogical.
Now for the mathematical proof I will appeal to a simple idea of mathematics - If you can provide at least 1 counterexample to a rule, that rule cannot possibly be true.
I'm gonna stay away from the logical fallacy of "dividing infinity an infinite number of times" because as I explained before this already doesn't make sense from a mathematical P.O.V.
“You can divide infinity an infinite number of times, and the resulting pieces will still be infinitely large. But if you divide a non-infinite number an infinite number of times the resulting pieces are non-infinitely small. Since they are non-infinitely small, but there are an infinite number of them, if you add them back together, their sum is infinite. This implies any number is, in fact, infinite.”
So, if you divide a non-infinite number an infinite number of times the resulting pieces are non-infinitely small.
Let's take our non-infinite number to be 1. (doesn't matter what value it actually is, I could've called it "x", but like this it's easier)
We are dividing an "infinite number of times" which means that we have 1/1, 1/2, 1/3, 1/4, 1/5, 1/6, 1/7 ... 1/∞ as our non-infinitely small pieces.
Since they are non-infinitely small, but there are an infinite number of them, if you add them back together, their sum is infinite.
Here is where the critical mistake is made. The claim is: an infinite number of non-infinite values added together sums up to infinity
Counter-proof: Our previous calculation left us with the series of 1/x where x -> ∞ (read as x tends to ∞).
lim[SUM(1/x)] = lim(1/1+1/2+1/3+1/4+...+1/∞) = lim (1/∞) = 0 (this is a proven theorem, if you don't believe me check WolframAlpha and compute it).
So the sum converges at 0, and not ∞. Why? Because you claimed that you're dividing a number P an infinite number of times, which means that although you might have a few values over 1 (i.e. x>y when you calculate x/y), most of them will be smaller than 1 (i.e. x<y when you calculate x/y).
This is a really ghetto solution because if I would've done it purely mathematical I was worried maybe you wouldn't get it.
The series that I used (1+1/2+1/3+1/4+...+1/∞) is called a Harmonic Series (http://en.wikipedia.org/wiki/Harmonic_series_%28mathematics%29#Divergence)
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This guy, what is he? O.o that was beautiful Mordred.
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This ever smaller theorem is what I have used to prove, at least in theory, that movement is not possible.
To get from point A to point B, you must first go through the midpoint at point C: A--C--B
But to get from point A to point C, you must first go through the midpoint at point D: A--D--C
and so on.
The are an infinite number of midpoint's that must be crossed in order to make forward movement, but for every midpoint there is an another one standing in the way, hence, movement isn't possible.
WE'RE ALL LIVING IN A DREAM!
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Obviously people have a hard time understanding the concept of limits.
You are refering to "Achilles and the tortoise", syk0b4bbl3.
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Obviously people have a hard time understanding the concept of limits.
You are refering to "Achilles and the tortoise", syk0b4bbl3.
Heh, limits sucked when I first learned them also. But after the millionth limit that you have to work on 30 minutes just to get it to a shape where it's not an illegality (i.e. 0/0) you kinda get the hand of it ;D
Yeah it's basically the same thing, only the explanation is a bit different. In "Achilles and the tortoise" the logical fallacy is the assumption that both Achilles and the turtle have the same frame of reference, which they don't.
In syk0b4bbl3's story actually you need the same stuff from the OP's question. It's a matter of dividing an infinite number of times and the same counter-proof that I wrote a few posts up applies.
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0**-1 = 1
BOOYAH!!!