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 fractionsargument, for countability.Regards,Ross Finlayson