```Date: Dec 30, 2012 4:04 PM
Author: ross.finlayson@gmail.com
Subject: Re: Uncountable Diagonal Problem

On Dec 30, 8:38 am, Shmuel (Seymour J.) Metz<spamt...@library.lspace.org.invalid> wrote:> In <Pine.NEB.4.64.1212300024480.22...@panix2.panix.com>, on 12/30/2012>    at 12:47 AM, William Elliot <ma...@panix.com> said:>> >A list of length eta, is a function from the ordinals < beta to a> >set of items.  Mega-sequence will be used as a synonym for list.>> Your definition of list is nonstandard. Why not use standard> nomenclature, e.g., ordinal-indexed sequence> <http://en.wikipedia.org/wiki/Order_topology#Ordinal-indexed_sequences>?>> >How long does a list without duplicates of infinite binary series> >(IBS)  have to be to force the list to have every IBS?>> C+1[1]>> [1] Next largest cardinal, not next largest ordinal.>> --> Shmuel (Seymour J.) Metz, SysProg and JOAT  <http://patriot.net/~shmuel>>> Unsolicited bulk E-mail subject to legal action.  I reserve the> right to publicly post or ridicule any abusive E-mail.  Reply to> domain Patriot dot net user shmuel+news to contact me.  Do not> reply to spamt...@library.lspace.orgFormulate Cantor's nested intervals with "mega-sequences" (ortransfinite sequence or ordinal-indexed sequence) instead of sequencesof endpoints.  Well-order the reals and apply, that the sequencesconverge yet have not emptiness between them else there would be twocontiguous points, in the linear continuum.  Note the identicalconsequences, as to well-ordering the reals by the naturals.Well-order the reals.Regards,Ross Finlayson
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