On 15 Jun., 18:46, stevendaryl3...@yahoo.com (Daryl McCullough) wrote: > WM says... > > > > >On 15 Jun., 16:32, stevendaryl3...@yahoo.com (Daryl McCullough) wrote: > >> 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 > > >As every n is finite, it belongs to a finite initial segment of the > >infinite list. > > I'm not sure what you are saying. The fact is, we can prove > that for every real r_n on the list, d is not equal to r_n.
Of course. Every real r_n belongs to a finite initial segment of the list. That does not yield any result about the whole list
> That means that d is not on the list. There is no extrapolation > involved.
Look here: We can prove for any finite segment {2, 4, 6, ..., 2n} of the ordered set of all positive even numbers that its cardinal number is surpassed by some elements of the set.
Nevertheless this appears not be a proof that the cardinal number of the whole set is less than some elements of the set.
Why should the extrapolation be more valid for Cantor's list?
