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