Date: Jan 15, 2013 3:42 AM
Subject: Re: Matheology § 191
On 14 Jan., 23:21, Virgil <vir...@ligriv.com> wrote:
> > yes, but never from all - since all possibilities are in the list -
> > like in the Binary Tree.
> So that in the wild weird world of WMytheology, though not elsewhere,
> one can have a thing which differing from each member of a list without
> differing from all members of that list.
Obviously. The reason is simple: There is no "all" for infinite sets.
> > Yes, it does and it does not. That's called a contradiction.
> But note that that only happens in WMytheology.
> Outside WMytheology, an infinite sequence differs from each of any set
> of finite sequences, if only by being infinite instead of finite.
That does not help. It can only differ at finite places. But since all
finite places belong to finite initial segments, and since all finite
initial segments are in the list, the anti-diagonal cannot differ from
all entries of the list. I know, it is hard for you to accept that,
but infinity does not help.
> But according to WM, within his wild wild world of WMytheology an
> infinite sequence can be identical to a finite sequence.
No, but the infinite sequence consists exclusively of finite initial
Didn't you know that? It is so.