Date: Jan 30, 2013 5:52 PM
Author: Virgil
Subject: Re: Matheology � 203

In article 
WM <> wrote:

> On 30 Jan., 12:02, William Hughes <> wrote:
> > Summary.  We have agreed that
> >
> > For a potentially infinite list L, the
> > antidiagonal of L is not a line of L.

> Yes, that is unavoidable. Up to any n, the diagonal differs from every
> antry.
> But if you assume that all terminating decimals can be enumerated and
> written in one list, then it is impossible that the antidiagonal
> differs from all of them at finitely indexed digits, because every
> finitely indexed digit belongs to a terminating decimal. And they are
> all in the list by definition.

That assumes, contrary to fact, that we are not allowed to have any
nonterminating decimals, even as antidiagonals, but outside of
Wolkenmuekenheim and inside of standard mathematics we ARE allowed do
have them, and so outside of Wolkenmuekenheim WM is dead wrong!
> >
> > The question is:
> > Does this imply
> >
> > There is no potentially infinite list
> > of potentially infinite 0/1 sequences, L,
> > with the property that
> > any potentially infinite 0/1 sequence, s,
> > is one of the lines
> > of L.

> What means "there is" with respect to potential infinity?

Any function from |N to {0,1} , of which there are a lot in standard
math, IS such a function. In standard mathematics, "potential
infiniteness" does not exist, but actual infinitness does,.

> In my opinion

Outside of your Wolkenmuekenheim, your opinion is irrelevant.

And the vast majority of mathematics and mathematicians live entirely
outside your weird world of Wolkenmuekenheim.