Date: Jan 14, 2013 4:09 PM
Subject: Re: Matheology � 191
WM <firstname.lastname@example.org> wrote:
> On 14 Jan., 00:00, Virgil <vir...@ligriv.com> wrote:
> > An infinitely long anti-diagonal can differ from a different listed
> > entry at each of its infinitely many places
> each of which belongs to a finite intial segment and hence is present
> in a sensibly constructed list.
it still differs from each of the listed elements.
> >Thus unless the list is
> > uncountably long, it can differ from all of the lists entries
> and it cannot differ from all entries if they were sensibly chosen.
But, nevertheless, it does.
> > I never "comprehend" claims that I have disproved.
> You have disproved the possibility of a list containing all finite
> initial segmenst?
Note that any list including finite sequences can be bijceted with a
list of infinite sequences by adding one "letter" to the alphabet of
those sequences and appending an infinite sequence of that letter to
every finite sequence.
Thus EVERY list of sequences is equivalent to a list of infinite
sequences, and the Cantor diagonalization method applies.