Date: Mar 31, 2013 12:53 PM
Author: fom
Subject: Re: Matheology § 224

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 withreal numbers according to the system of continuedfractions.