Date: Mar 31, 2013 12:49 PM
Author: ross.finlayson@gmail.com
Subject: Re: Matheology § 224

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 thegeneral property of a space being Baire, consider whether there areordinals 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 cardinalsbetwen those of N^n and N^N?  Because, cardinals have initialordinals.  Are there limit ordinals between those of w^n and w^N?Obviously enough it's consistent with ZF that there are, though, thereare none between n, for all n e N, and N.Then, compared to the language of the expansions of 2^w from thealphabet {0,1} as (0|1)\infty, items from N^N are in a language  (n eN)\infty.What's the 1-1 and onto function from 2^w to N^N?Then, apply EF or sweep to it.Thanks,Ross Finlayson