WM says... > >On 15 Jun., 12:39, stevendaryl3...@yahoo.com (Daryl McCullough) wrote: > >> That's *all* that matters, for Cantor's theorem. The claim >> is that for every list of reals, there is another real >> that does not appear on the list. > >The claim is only proved for every finite subset of the list.
The proof does not make use of any property of infinite lists. The proof establishes: (If r_n is the list of reals, and d is the antidiagonal)
forall n, d is not equal to r_n
There is no "extrapolation" involved. The way that you prove a fact about all n is this:
Prove it about an unspecified n. Use universal generalization.