Date: Feb 1, 2013 7:22 PM Author: Virgil Subject: Re: Matheology � 203 In article

<f3053338-8811-41fa-bac6-c9b090d2139d@k4g2000yqn.googlegroups.com>,

WM <mueckenh@rz.fh-augsburg.de> wrote:

> On 1 Feb., 10:58, William Hughes <wpihug...@gmail.com> wrote:

> > On Feb 1, 10:37 am, WM <mueck...@rz.fh-augsburg.de> wrote:

> >

> >

> >

> >

> >

> > > 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.

> >

> > Yes, but every does not describe the list but the

> > potentially infinite set of potentially infinite

> > 0/1 sequences.

> >

> > Please answer the question.

> >

> > Let s be a potentially infinite

> > 0/1 sequence.

>

> How do you define this sequence? Has it a finite definition?

Such sequences have just as much of a finite definition as your

potentially infinite sets of naturals do.

> >

> > Does this imply that there is

> > a natural number m, such that s

> > is the mth line of L-

>

> There are many lists that lack many sequences. For instance the list

> 0.1

> 0.11

> 0.111

> ...

> lacks all sequences with zeros.

But is, in fact, totally and finitely definable, given |N, but nonsense

without an |N.

Note that in any proper set theory, potential but not actual "sets" are

not really sets until they can be made actual.

Shouldn't we label them pseudosets?

--