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 > >  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.org
Formulate Cantor's nested intervals with "mega-sequences" (or transfinite sequence or ordinal-indexed sequence) instead of sequences of endpoints. Well-order the reals and apply, that the sequences converge yet have not emptiness between them else there would be two contiguous points, in the linear continuum. Note the identical consequences, as to well-ordering the reals by the naturals.