presley@mhuxj.UUCP (09/16/83)
Since we're all into fallacious proofs, how about the following: x = 1 + 2 + 4 + 8 + 16 + ... = 1 + 2(1 + 2 + 4 + ...) = 1 + 2x x = -1 Q.E.D. -- Joe Presley (mhuxj!presley, harpo!presley)
ecn-ec:ecn-pc:ecn-ed:vu@pur-ee.UUCP (09/17/83)
That is just as dumb as saying: inf = 2 (inf) ----> inf = 0. Of course you cannot cancel "infinity" both sides ! The simple reason is that "infinity" is not a number, but merely a short-hand; that is saying x(n) ---> inf [where x is some sequence] is a short hand for "For all integer N, there is a natural number n such that |x(n)|>|N|" where | | denotes absolute value. Hao-Nhien Vu(pur-ee!norris)
dce@tekecs.UUCP (David Elliott) (09/18/83)
All numbers are equal to infinity. I've always said that infinity is "the number that fits". 0/x = infinity because it fits. David
dje@5941ux.UUCP (09/21/83)
Response to the paradox of:
x = 1 + 2 + 4 + 8 + ...
= 1 + 2 * (1 + 2 + 4 + ...)
= 1 + 2 * x
implying x = -1.
The series (1 + 2 + 4 + ...) doesn't sum to any real number, so saying that
"x = 1 + 2 * x" doesn't give you the license to infer that x = -1.
If you try to tinker with "infinite" quantities as if they were numbers,
then you can get all kinds of inconsistent "equalities" like x = x + 1 as well.
Dave Ellis / Bell Labs, Piscataway NJ
...!{hocda,ihnp4}!houxm!houxf!5941ux!dje
...!floyd!vax135!ariel!houti!hogpc!houxm!houxf!5941ux!djepga@ritcv.UUCP (Peter G Anderson) (09/23/83)
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