Virgil
Posts:
4,482
Registered:
1/6/11
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Re: Matheology � 203
Posted:
Feb 1, 2013 7:22 PM
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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?
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