That is kind of like saying pi = 3.14 exactly, but 0.9999 is just 0.9999 unless you round it, but rounding is for lazy gay people such as your friend.
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Anonymous2008-08-23 5:49
He is correct.
He is also gay.
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Anonymous2008-08-24 1:17
I think he meant 0.9999999 recurring
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Anonymous2008-08-24 1:22
Yeah, recurring or not, it doesn't equal 1, rounding it will make it equal one. If logic like that was applied to bigger numbers then why even have the number 9 if just equaled 10? That is pretty much what OP's gay friend is saying.
0.9999999999999~ in no way equals 1, it just rounds to it, yes it is very close 1, but does not equal it.
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Anonymous2008-08-24 1:25
>>6
OP here, that is exactly how I understood it, but the whole 1/3, 2/3, 3/3 deal makes it confusing
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Anonymous2008-08-24 3:35
actually 0.999 where 9 is recurring does indeed equate to 1.
it can be proven via simple algebra.
let equation 1 be x=0.999~
now, let equation 2 be 10x = 9.9999~
.999999~ means "sum as i goes from 1 to Infinity of 9/10^i". A sum to infinity is defined as the limit of partial sums, and we all agree that the limit is 1.
QED
Another proof:
One of the axioms of the real numbers states that between any 2 real numbers, there are an infinite number of other real numbers. Let S = .99999~ and let T = 1. Assume they were unequal. Then they would have a positive real number as the difference, W. But for any real number you pick, the difference is less than your number(intuitively, just "increase the number of 9s"). The only real number less than all positive numbers is 0.
QED
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Anonymous2008-08-24 20:57
>>6
This makes me rage, if you were serious. If not, then, carry on.
>>9
learn to fuckin' spell >>11
1st point, who made you boss and let you say that those symbols had to mean a sum
2nd point, who said those symbols were a fuckin' number