Date: Feb 3, 2013 5:09 PM
Author: William Hughes
Subject: Re: Matheology § 203

On Feb 3, 10:58 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
> On 3 Feb., 22:29, William Hughes <wpihug...@gmail.com> wrote:
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> > > > We can say  "every line has the property that it
> > > > does not contain every initial segment of s"
> > > > There is no need to use the concept "all".
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> > > Yes, and this is the only sensible way to treat infinity.
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> > So now we have a way of saying
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> > s is not a line of L
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> > e.g.  0.111...  is not a line of
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> > 0.1000...
> > 0.11000...
> > 0.111000....
> > ...
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> > because every line, l(n),  has the property that
> > l(n) does not  contain every  initial
> > segment of 0.111...
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> But that does not exclude s from being in the list.

It certainly excludes 0.111... from being a single line
of the list.

So the question is now

Can a potentially infinite list
of potentially infinite 0/1
sequences have the property that

if s is a potentially infinite 0/1
sequence, then there is a line, g, of L
with the property that every
initial segment of s is contained in g
?