Date: Mar 31, 2013 1:04 PM
Author: ross.finlayson@gmail.com
Subject: Re: Matheology § 224

On Mar 31, 9:53 am, fom <fomJ...@nyms.net> wrote:
> On 3/31/2013 11:49 AM, Ross A. Finlayson wrote:
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> > On Mar 31, 9:17 am, fom <fomJ...@nyms.net> wrote:
> >> On 3/31/2013 10:52 AM, Ross A. Finlayson wrote:
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> >>> Well, you see Virgil has introduced a term in context the "binary
> >>> rational path":  in cooperative communication that is so defined
> >>> there, because that every initial segment is the initial segment of a
> >>> rational, and that the language of "rational paths" is unbounded,
> >>> doesn't offer for him the conclusion of his arguments.  So, he expects
> >>> that to be understood as his definition in passing, or he can point to
> >>> it later, as to differentiating his personal definition from the
> >>> general definition, as so qualified.

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> >> Yeah.
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> >> He should not have done that.
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> >> The Baire space has the required property in
> >> relation to rational numbers -- correspondence
> >> with eventually constant sequences.

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> >> It gets confusing when you are trying to deal
> >> with WM's misrepresentations.

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> > Where "the" Baire space for Rene-Louis Baire is N^N as opposed to the
> > general property of a space being Baire, consider whether there are
> > ordinals between n, for any n in N, and N.  N^n <-> N, N^N <-> P(N).
> > if there are no ordinals between n and N, are there no cardinals
> > betwen those of N^n and N^N?  Because, cardinals have initial
> > ordinals.  Are there limit ordinals between those of w^n and w^N?
> > Obviously enough it's consistent with ZF that there are, though, there
> > are none between n, for all n e N, and N.

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> > Then, compared to the language of the expansions of 2^w from the
> > alphabet {0,1} as (0|1)\infty, items from N^N are in a language  (n e
> > N)\infty.

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> > What's the 1-1 and onto function from 2^w to N^N?
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> The elements of the Baire space coincide with
> real numbers according to the system of continued
> fractions.


Thank you, I already covered a case for EF and the continued fractions
argument, for countability.

Regards,

Ross Finlayson