Re: Cantor's circular "proof" that evens = integers

On Sat, 05 May 2007 09:11:59 GMT, Phil <toob-headman@xxxxxxxxxxxxx>
wrote:


Now, if anyone can PROVE that whenever x is in N, then 2*x is in N,
then you have a true PROOF that N and E are equinumerous.

If you weren't the idiot you are, you might notice that * is an
operation which can be (and is) defined in set theory, such that
n*m in N for all n,m e N. Since 2 e N this implies that 2*n in N
for all n e N.

If you are curious, * is defined the following way:

(a) n * 0 = 0
(b) n * m' = n * m + n


However, simply claiming that "this is obvious" is not adequate [...]

No-one (other than you) suggests that the claim "this is obvious"
is an adequate replacement for an explicit mathematical proof.

Actually, WE all know that

"Unproven statements carry little weight in the world
of mathematics." (Amir D. Aczel)


F.


For more information see:
http://en.wikipedia.org/wiki/natural_numbers

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