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Post by
HighFive
That is not true, Wiki, and you know it.
edit: Dealing with infinity is tricky. Infinity seems to defy many of the truths, intuitively associated with finite objects.
Some food for thought:
Even numbers seem to be exactly half of all natural numbers, but are they not actually the same amount?
Prime numbers are even rarer, yet there is an infinite number of them as well. A "smaller" infinity perhaps?
Are there more whole numbers than there are natural ones?
Are there more rational numbers than there are whole ones?
Are there more real numbers than there are rational ones?
Are there more complex numbers than there are real ones?
edit2: @WonderingFox:
Which of the following statements do you actually disagree with?
1) 1 = 3/3
2) 1/3 = 0.(3)
3) 3 * 0.(3) = 0.(9)
It would seem to me that if none of these is wrong, we can conclude that 1 = 0.(9) with clear conscience.
Also, I am curious as to your understanding of 0.(0)1. What is this number? How is it defined?
edit4:.(9) + .(9) = 1.8(9)How did you get this result? Does the carry not make it 1.(9)?
Also, 0.(9) + 0.(9) = 0.9 + 0.0(9) + 0.9 + 0.0(9) = 1.8 + (0.(9) + 0.(9)) / 10 = 1.8 + (1.8 + (0.(9) + 0.(9)) / 10) / 10 = 1.8 + 0.18 + (0.(9) + 0.(9)) / 100 = 1.98 + (0.(9) + 0.(9)) / 100.
Post by
Wikipedia
I read it somewhere, and I've heard it from several friends. Not that I have a clue for how it actually can be...
Post by
Wanderingfox
x dx
.(9) dx = 1
1 dx = 0
I believe. It's been a LOOOONG time since I've dealt with derivatives with any regularity, and I could be misremembering (which is why I removed it)
# 3 would have to = 1 for his statment to be true, but it doesn't. Thus his statement is false.
0.(0)1 I was just using the conventionally adapted notation so far to illustrate the idea of the hypothetical missing part. ie. if .(9) + x = 1 then x = 1 - .(9). This value is not 0, but rather is an infinity small number.
This whole thing boils down to our definition of infinity. While simple in concept, it is flawed fundamentally. Specifically in the sense that anything + infinity = infinity, which while this fits the definition of infinite (pouring water into a full cup does not make it 'fuller'), goes against basic mathimatics (the excess water just poofs out of existence?).
If you look at it from a logical point of view, rather than purely mathematic one, you'll quickly come to the conclusion that the word infinite, in and of itself, is flawed.
Consider the following thought experiment.
I have a faucet that puts out an infinite amount of water. I decide to collect this water in an infinitely large measurable tank. I do the same thing with a second faucet and tank, except that this second tank starts with 10 gallons of water in it already. Since both faucets put out the same (infinite) amount of water at the same rate, both tanks should be equal when measured (.9 repeating = 1). However, logically this will not be true since tank #2 started with more in it initially (.9 repeating =/= 1). No matter how long I wait, tank 2 will always have more water.
edit 4:
Does the carry not make it 2 then? You're suggesting that you made an infinite number finite. I was retaining the .(9)
Post by
HighFive
@Wikipedia: You may have heard that 2^infinity > infinity, which is true for a certain notion of infinity and a certain notion of exponentiation, and a certain notion of comparison (edit: and a certain notion of 2).
@Wanderingfox: Your thought experiment does not accurately represent the issue of hand. You are measuring finite amounts of water. Will the two tanks not hold equal amounts after an infinite amount of time has passed and all of the watter has been poured into them?
edit:Does the carry not make it 2 then?Yes, because 0.(9) = 1. :rolleyes:
You're suggesting that you made an infinite number finite. I was retaining the .(9)I don't see what you are referring to. Can you clarify?
Post by
Wanderingfox
Point 1: If we, for a moment, assume that .(9) =/= 1 then .(9) + .(9) = 1.8(9) you have to ROUND this number to make it 2.
Point 2: For each pair of 9's you generate an 18.... this means that this theoretical infinite number ends in an 8... not a 9. By your own admission, .(9) = 1 then 2 = 1 + .(9), which again by your own admission should end in a 9, yet basic rounding says it should end in an 8.
Point 3: .(9) + .(9) equals both 2 and 1.(9) in your statement. In this case, one number is representing multiple values.
Post by
HighFive
@Point 1: I am still curious on your infinite arithmetics. Can you walk me through the process you got that result through?
(is it time I whip out the definitions and analysis?)
@Point 2: Infinity doesn't "end". That is all.
@Point 3: Actually, I claim that 2 = 1.(9). There is only one multiple value.
Post by
Wanderingfox
Infinity doesn't "end".
Case and point. Then infinity cannot be rounded, which means you cannot use it in your argument whenever .(9) is in fact infinite. If that is the case, .(9) is finite, and therefore is not equal to 1.
Also, if x = ...999 then 10x = ...990, so 10x = x − 9, hence x = −1
edit:
The above was a diversion from the exact problem from before, I'm trying to illustrate that the concept does not fit into conventional mathematics.
@@Point 3: Then 1 + 1 = 1.(9) then? or does 1 not exist? is it replaced by .(9)? What does all this mean for 2? Numbers are vanishing in your interpretation.
Post by
janniie
if x = ...999 then 10x = ...990, so 10x = x − 9, hence x = −1
By saying that ...999 * 10 = ...990 you are yet again that infinity is finite.
Post by
248766
This post was from a user who has deleted their account.
Post by
Wikipedia
pHish, wanna come over for dinner? I feel lonely...
Post by
248766
This post was from a user who has deleted their account.
Post by
Wikipedia
Yeah, all since Krow went berserk and tore me to pieces I've been feeling somewhat depressed...
Post by
kamii
Another great day at work. In the worst case I am in national news with our prime minister and I looked like shiat. :(
Post by
Wikipedia
You know, we do want to see that? So hook us up with some livestream footage of that newscast!
Post by
kamii
Well, frankly I can't record it and I doubt it's going online (unless there are some creeps who youtube everything related to our "whole body" minister, and I wouldn't be surprised either)
Post by
Wanderingfox
if x = ...999 then 10x = ...990, so 10x = x − 9, hence x = −1
By saying that ...999 * 10 = ...990 you are yet again that infinity is finite.
the number is still infinite, just terminating. If you define something as .(9) as possible then it ends at the decimal point. I simply reversed this notion stating that it is infinite in the other direction ie. (9).0 instead. You're selectively applying the theory you're trying to prove. This, in and of itself, is not correct. You cannot state that your proof is true and then selectively ignore the parts of it that are not. If .(9) is infinite to the right than (9).0 is infinite to the left.
Yet again, you ignore basic mathematics in order to attempt to prove your point. Just because something extends forever in a direction (by your own admission the definition of infinite) does not mean it doesn't have a terminating point. If you want your proof to work, prove that it functions for something that does not terminate on either end.
Your 'proof' is taking advantage of a selective rounding error in mathematics. Logically your proof is flawed. Mathematically, your proof is limited to specific examples. If your proof were truly correct, it would function for all cases.
If we actually logically define what .(9) is, it is a number that is infinitesimally close to 1. It is really, really,
REALLY
close to 1, but it is also infinitesimally off. For all practical applications of this they will result in the same answer. This is because it is impossible to mathematically work with an infinite number without losing precision... and the second you lose precision this entire proof fails to function. This means the second you add, subtract, multiple, divide or do ANYTHING to the number, you've defined it as finite because, yet again by your own admission, infinity + infinity = infinity. Thus .(9) + anytihng is still .(9) unless you contradict your own proof, and/or admit to the fact that .(9) (and thus ...999) terminate.
If they terminate, which they must at at least one end (see previous paragraph) then my simple math proves that x can equal ...999 and -1 at the same time, QED your theory is incorrect.
edit:
To distill this whole argument down, and mostly because we're just going around in circles here...
.(9) is equal to 1 for any and all cases where precision is terminated. This happens in just about all practical cases of mathematics because its impossible to actually perform any operation on a truly infinite number without losing something in the process... ie. infinity + 2 = infinity.
However, the second .(9) terminates due to the above, everything to the right of the termination rounds, making it equal 1.
Your claim is that .(9) is logically equal to 1. This is not true. If we suggest that there are an infinite number of numbers between 0 and 1 then simple logic dictates that .(9) < 1. The only way for it to be logically equal to 1 would contradict the logical definition of .(9) (a number that is i finitely
close
to 1).
In short, we're both correct in some manner. Your proof functions because the mathematical flaw that allows it applies to all of mathematics. This notion is like trying to do base 2 math with 3 numerals. Since this flaw exists both in your proof (which your proof exploits) as well as in all possible counter proofs, there only way to counter-prove yours mathematically is to omit the flaw (my ...999 argument). Logically, however, your answer does not make sense given the previous definitions of both infinite and .(9)
So yes, if .(9) is truly infinite, for all intents and purposes, it counts as 1. However, it is so infinitesimally off that the theoretical missing piece will never be noticed. Take, for example, someone taking a single drop of water out of the ocean. No one will
ever
notice, but that piece is still theoretically missing.
Post by
pelf
Everyone should read kamii's signature
:)
.
Post by
Wanderingfox
ewww xperl?
Post by
TheReal
Take, for example, someone taking a single drop of water out of the ocean. No one will
ever
notice, but that piece is still theoretically missing.
Since we're discussing the infinite, I think it would be more like taking a quark from the universe. But if you did that, where would you put it?
Post by
HighFive
I would put it in my pocket with all the other quarks I've collected.
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