OP, do some research, stay the fuck off this board until you are convinced that 0.9~ is exactly 1, and never ever consider ever asking if 9999/10000 is 1, or even if 999999999999999999/10000000000000000000 = 1
wikipedia/0.999...
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Anonymous2007-09-02 17:19 ID:zSY5ncPz
wtf kind of question is that?
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Anonymous2007-09-02 17:24 ID:EsIu42f3
"wtf kind of question is that?"
It is one that demands an answer, young padewan.
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Anonymous2007-09-02 18:02 ID:OSeDWSBs
EVERYONE agrees it is both true and false. It's a question of philosophy if you believe it or not.
x = 0.9~
10x = 9.9~
9x = 10x - x = 9.9~ - 0.9~ = 9
qed
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chris2007-09-02 18:52 ID:o6N1T5au
wow i was honestly convinced that .99999999999... is one because there are an infinite number of nines. if you disagree you simply dont understand the concpet of inifnity, lol
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chris2007-09-02 18:53 ID:o6N1T5au
very nice proof by the way... best one i've seen
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Anonymous2007-09-02 19:11 ID:z3exrY2z
Unfortunately, one of the worst there is, as far as rigor goes.
1-(1*10^-∞) where (1*10^-∞) ≠0 , so 1-(1*10^-∞)≠1-0, so 1-(1*10^-∞)≠1 and finally 0.9~≠1
The fact on experimental measurement 0.9~=1 its just because it doesn't matter, they are NEARLY the same and theres infinitesimal difference between them. But mathematically they are not the same for obvious reasons.
Say you have a perfectly round pie. You take an infinitely small slice from that pie. Is it still a whole pie?
Here's an easier one to grasp, using exponentials. Say you have two graphed points, point A and point B. You move point B half way closer to point A, to shorten the distance between them by half, so they are %50 as far from each other as before. Say you take away half the distance between them once more...and once more...and once more...and so on. The points will keep getting closer to each other each time, but they will never meet, no matter how many times you divide by half. And, as the distance between the points will never reach zero after dividing the distance in half infinity times, 0.9~ will never equal 1. It will keep getting closer, but never get there.
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nurr2007-09-04 3:08 ID:AwkU5fof
>>23
we have this thing called infinity in math.. and the proof of this uses exactly your argument, plus infinity. The idea is that of a limit. We say that .999... approaches 1. That is to say, the distance from .999 to 1 decreases to 0 as n goes to infinity. There's no number less than 1 that is greater than .999... Just try to think of one.
We say that the series 9/10^n converges to 1 as n goes to infinity. When we write down an infinite series like 1/3=.333... or 1=.999..., what we are expressing is the limit, that number that the series converges to.
To use your pie example, let's say we had a pie of area 1 and somehow broke it into an infinite number of pieces, with each piece's area equal to 9/10^n, where n goes from 1 to infinity. Do the areas of all those pieces add up to 1?
This isn't up for argument. It follows logically from accepted axioms.
after sleeping on the matter, my mind is basically changed. I wasn't countering in genuine infinity before (it is, after all, very difficult to conceptualize).
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Anonymous2007-09-04 15:41 ID:IDQS41rs
>>31
We don't know what >>30 is intending after the 1, actually.