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:

>

>

>

>

>

>

>

>

>

> > On Mar 31, 9:17 am, fom <fomJ...@nyms.net> wrote:

> >> On 3/31/2013 10:52 AM, Ross A. Finlayson wrote:

>

> >>> 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.

>

> >> Yeah.

>

> >> He should not have done that.

>

> >> The Baire space has the required property in

> >> relation to rational numbers -- correspondence

> >> with eventually constant sequences.

>

> >> It gets confusing when you are trying to deal

> >> with WM's misrepresentations.

>

> > 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.

>

> > 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.

>

> > What's the 1-1 and onto function from 2^w to N^N?

>

> 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