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RE: Wait what? (1+2+3+4+... - Bridge - 01-14-2014
(01-14-2014, 02:34 AM)Chronofrog Wrote: 0.999... is not a number with nonzero decimals, despite how it looks when it is written.
Okay, so if you write a googolplex to the power of googolplex of 9s the distance between 0.999... and 1 is just absurdly small, but if you keep going forever it magically stops existing? Again, traditional mathematics aren't designed to treat infinity as meaningful data (because it is meaningless). Shaving off an infinitesimal, which by definition is infinitely small and yet not zero, is simplification. It's not a "proof" that should be regarded as gospel, in my opinion. I mean, just because your understanding of the natural world dictates that the infinitesimal is unknowable doesn't mean you can assume it's zero.
RE: Wait what? (1+2+3+4+... - BAndrew - 01-14-2014
@Chronofrog
So briefly, you agree with me.
@Bridge
How does this sum have a valid proof? The proof is incorrect and creates a lot of errors like the ones I mentioned.
On the other hand 0,9999... = 1 has a valid proof:
![[Image: 6fa510b44742046a167b4b8515162825.png]](http://upload.wikimedia.org/math/6/f/a/6fa510b44742046a167b4b8515162825.png)
Quote:I still persist that the proofs offered to support it are facile.
Can you disprove it or find an error in the current proof or not? If you can't then you have to assume it is correct.
RE: Wait what? (1+2+3+4+... - Bridge - 01-14-2014
(01-14-2014, 02:01 PM)BAndrew Wrote: The proof is incorrect and creates a lot of errors like the ones I mentioned.
And conflating infinitesimal values with zero is not an error in your opinion? Those 9s go on endlessly, you never reach 1. The proof flat out assumes that the distance between 0.999... and 1 is 0. I don't call that proof.
RE: Wait what? (1+2+3+4+... - BAndrew - 01-14-2014
Where exactly in the proof is the assumption you talk about?
Another much simplier proof that I've found is this:
It uses the following theorem that can be proved.
If |r|<1 then ar + ar² + ar³ + ... = a*r/(1-r) (infinite sum of geometric series)
![[Image: 56949181a290ce561f27bd550a720392.png]](http://upload.wikimedia.org/math/5/6/9/56949181a290ce561f27bd550a720392.png)
Another proof:
We assume that 1 =/= 0,999... =>
(devide by 3) 1/3 =/= 0,333... absurd
Therefore 1=0,999...
RE: Wait what? (1+2+3+4+... - Bridge - 01-14-2014
1 - lim(n->inf) 1/10^n = 1
I have not seen any convincing evidence to support the claim that 1/inf is 0. Yet this proof goes ahead and assumes that. It's infinitely small, so it gets smaller and smaller until the end of time. It doesn't just stop existing. How anybody can accept that is beyond me. I'm not arguing on the basis of mathematics here, so don't bother throwing proofs at me (I've seen most of them).
Say you are cutting a piece of paper, each time by exactly half (ignoring what it is made up of, assume that it is always possible to halve it). If you had a microscope that was capable of zooming in an infinite amount and access to tools that were infinitely small, would you ever reach a point where the paper disappears?
RE: Wait what? (1+2+3+4+... - BAndrew - 01-14-2014
(01-14-2014, 04:41 PM)Bridge Wrote: 1 - lim(n->inf) 1/10^n = 1
I have not seen any convincing evidence to support the claim that 1/inf is 0. Yet this proof goes ahead and assumes that. It's infinitely small, so it gets smaller and smaller until the end of time. It doesn't just stop existing. How anybody can accept that is beyond me. I'm not arguing on the basis of mathematics here, so don't bother throwing proofs at me (I've seen most of them).
Bolded:
If that is true then you should know that:
lim.(1/x) = lim.(1/x) = 0
x-->+∞...x-->-∞
It's basic calculus that you (probably) learn on high school. I am not assuming anything, nor does the proof.
Underlined: If you have seen the other proofs then is there something wrong with them?
RE: Wait what? (1+2+3+4+... - Bridge - 01-14-2014
(01-14-2014, 04:46 PM)BAndrew Wrote: Underlined: If you have seen the other proofs then is there something wrong with them?
They contradict the way in which I perceive the universe. Certainly you don't deny that all results are highly dependent on the methods you use to test them. It's possible, and examples abound, to get an ostensibly valid result even if you feed in garbage data. To my puny plebeian brain that is incapable of perceiving infinity, 0.999… = 1 is one such example. Lim(n->inf) is placing an arbitrary limit on something that is by definition limitless. If you still don't get it then I won't bother responding again. This is getting very tiring.
EDIT: There is some good, if chaotic, discussion here if you wish to read:
http://en.wikipedia.org/wiki/User:ConMan/Proof_that_0.999..._does_not_equal_1
I'm not responsible for anything anybody says there, so don't come back here with examples of faulty reasoning trying to refute me. I haven't even read most of it, but it is uncensored discussion.
RE: Wait what? (1+2+3+4+... - Froge - 01-14-2014
(01-14-2014, 02:01 PM)BAndrew Wrote: @ChronofrogWhy briefly?
So briefly, you agree with me.
RE: Wait what? (1+2+3+4+... - eliasfrost - 01-14-2014
How do you calculate with something that is infinite? I'm no math-head but it seems like infinity is something that can't be measured and therefore have no place in a calculation? Or maybe I'm too stupid?
RE: Wait what? (1+2+3+4+... - BAndrew - 01-14-2014
(01-14-2014, 05:03 PM)Bridge Wrote:(01-14-2014, 04:46 PM)BAndrew Wrote: Underlined: If you have seen the other proofs then is there something wrong with them?
They contradict the way in which I perceive the universe. Certainly you don't deny that all results are highly dependent on the methods you use to test them. It's possible, and examples abound, to get an ostensibly valid result even if you feed in garbage data. To my puny plebeian brain that is incapable of perceiving infinity, 0.999… = 1 is one such example. Lim(n->inf) is placing an arbitrary limit on something that is by definition limitless. If you still don't get it then I won't bother responding again. This is getting very tiring.
Then perhaps the way you perceive the universe is wrong? Just because you think something is true doesn't mean it is (eg I can believe that 1+1=3, but that is not true). You are not providing any proof of your statements (or disproof of 0.999...=1). You are basing your assumptions on your intuition although you can't prove/disprove anything. It's like saying "Whatever proof you provide I won't believe it because I don't like it".
Also, have you ever taken a course in calculus? Because saying that:
Quote:Lim(1/n->inf) is placing an arbitrary limit on something that is by definition limitless.means you haven't properly understood what the limit is. What you wrote reads:
The limit of 1/n as n approaches infinity equals 0. Nothing more, nothing less.
(01-14-2014, 05:11 PM)Chronofrog Wrote:I "summed up" your whole post in one sentence.(01-14-2014, 02:01 PM)BAndrew Wrote: @ChronofrogWhy briefly?
So briefly, you agree with me.
(01-14-2014, 05:17 PM)Naked? No Wrote: How do you calculate with something that is infinite? I'm no math-head but it seems like infinity is something that can't be measured and therefore have no place in a calculation? Or maybe I'm too stupid?
You can't calculate infinity, but it is used in calculations