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#1 Re: This is Cool » 0.9999....(recurring) = 1? » 2008-04-15 05:10:06
Wow, my bad. I can't believe I actually wrote that down... It was late, and I was tired.
But as for the difference being "0.000...1", I was merely saying that you can get any absurd answer you want when you're working with numbers that can't exist in the first place.
However, it is possible to 'reach' infinity if you do something for an infinite amount of time... like writing 9's on an infinitely long sheet of paper. No matter how many days, years, millenia, infinities you do that for, it will never ever change to one.
Never > Infinity.
#2 Re: This is Cool » 0.9999....(recurring) = 1? » 2008-04-14 17:02:51
As long as we're working with non-existent numbers here:
1
-
0.999...
_______
0.000...1
Ooooo, sorry. I went ahead and posted a topic about this and didn't realize it was already here (although, why wouldn't it be...). I'll just paste my squabble in here and you can all ignore my separately posted topic.
Ctrl+V!!
____________________________________________________________
So my roommate and I were talking the other night and ended up arguing for 3 hours about why or why not "0.999..." = 1. We came up with some interesting points. I'd like to point out why I believe it doesn't.
1:
1 X 2 = 2
0.9 X 2 = 1.8
0.99 X 2 = 1.88
0.999 X 2 = 1.888 and so on and so forth, so
0.999... X 2 = 1.888...
because no matter how many 9's you add to it, you will always end up adding that many 8's .
Okay, I was tired... and didn't think about what I was typing just there...
2:
The structure of numbers.
For any number, let's say "5", you can add anything to the places after it and no matter how many of anything you add you will never end up changing the numbers place previous to whatever you are adding at that time.
5
53
534
5341
53417
No matter how far I go, nothing I do can change the initial 5. Ever.
Saying that you're adding an infinite number of 9's to the end of "0.9" can never change the initial 9 laid down there. You will always end up with a "0.9" with a long string of numbers after it. Even infinity can't change that.
What I've heard is that there is no definable difference between "0.999..." and 1, therefore they are equal. I must agree that there can be no difference because no matter how many times you subtract "0.999..." from 1 you will always get "undefined". This does not mean their difference is "0", it only means we cannot calculate with "0.999..." because it is not a number and can never be a number. Infinity can't exist no matter how many ways we want to try and comprehend it. So introducing it into a number is about as useful as saying, "Chair = 8".
However, if you'd like to think of it as a real number, the arguments above apply and therefore there is a difference! 
In conclusion, we cannot make assumptions about a number just because we cannot comprehend it *yet... The world is still not flat.
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