Date: Feb 1, 2013 4:37 AM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: Matheology § 203

On 1 Feb., 09:35, William Hughes <wpihug...@gmail.com> wrote:
> On Feb 1, 9:21 am, WM <mueck...@rz.fh-augsburg.de> wrote:
>
>
>
>
>

> > On 31 Jan., 18:44, William Hughes <wpihug...@gmail.com> wrote:
>
> > > On Jan 31, 4:34 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
>
> > > > On 31 Jan., 16:15, William Hughes <wpihug...@gmail.com> wrote:
>
> > > > > > Would you say that a line that is not in the list is in the list?
>
> > > > > Nope. But you did.
>
> > > > Yes, but for an actually infinite list.
>
> > > What actually infinite list?
>
> > > Specifically you said
>
> > > A potentially infinite list, L,
> > > of potentially infinite 0/1 sequences
> > > can have the property that every
> > > (in the sense of "all from 1 to n")
> > > potentially infinite 0/1 sequence
> > > is a line of L?

>
> > > No actually infinite lists here
>
> > And what is your question please? Of course every line between line 1
> > and line n is in the list.

>
> Let a potentially infinite list, L,
> of potentially infinite 0/1 sequences
> have the property that every
> (in the sense of "all from 1 to n")
> potentially infinite 0/1 sequence
> is a line of L?


A potentially infinite list does not contain every whatever in the
sense of all. Because a list that in contains all whatevers is actual
with respect to these whatevers.

But of course the list contains every sequence that is a line between
1 and n (including the limits) and therefore contains all these
sequences.

These two meanings have to be distuingusihed carefully. Example: A
potentially infinite set of natural numbers does not contain all
natural numbers. Otherwise it would be an actually infinite set, namel
|N.

Regards, WM