Date: Mar 18, 2013 4:48 PM
Subject: Re: Matheology � 224
WM <email@example.com> wrote:
> On 18 Mrz., 00:59, Virgil <vir...@ligriv.com> wrote:
> > Why does WM claim that after what WM calls "Cantor's list" has been
> > diagonalized, he can include all anti-diagonals, when it is always
> > possible to find others that have been so far overlooked?
> This simply and exactly shows that it is inconsistent to assume one of
> both powers to be stronger.
> Every list yields another diagonal.
> And every diagonal can be included in another list.
> Both these facts are the two sides of infinity. Cantor did that false
> step to choose one as more justified than the other.
The issue here is whether some list can be so complete that no diagonal
can be constructed that is not already in it.
The answer, conceded above, is a resounding "NO"!
Which establishes, as required, that there is no surjection from the set
of all naturals to the set of all such listable sequences.
Thus WM concedes the proof of Cantor's diagonal argument.