```Date: Dec 31, 2012 11:05 AM
Author: ross.finlayson@gmail.com
Subject: Re: Uncountable Diagonal Problem

On Dec 30, 9:48 pm, Virgil <vir...@ligriv.com> wrote:> In article> <379c8a07-1e79-42ca-93e0-494f6444a...@pp8g2000pbb.googlegroups.com>,>  "Ross A. Finlayson" <ross.finlay...@gmail.com> wrote:>> > Here, I was wondering that for nested intervals in the transfinite,> > that the interval wouldn't be empty for two different endpoints (else> > it could be for a countable ordinal), that there would be a duplicate,> > i.e., that the well-ordering of the reals could be onto yet not 1-1.>> That looks a bit like English, but not at all like mathematics.>>>> > Of course I think EF is a function with range [0,1], that well-orders> > the unit interval of reals, with the caveat as above that it follows> > from an expanded definition of real number, while of course that it is> > standardly modeled by real functions.>> Ross mentioning his alleged "EF" shows him to be "EF"ing crazy!> --It's an acronym read and spoken "E.F.".  The natural/unit equivalencyfunction, N/U E F, may as well be called NUE, NUE(n), or EF.	E -> F, Empty -> FullI dispute that Hancher - as do others who find the deliberationsinteresting - and mathematical - again your blathering caws servenothing but to demean the discourse.  We already have the edifice ofmodern mathematics for ready reference, again your ad hominem attackshave no place in a mathematical discussion, on mathematics, and thereader easily finds them as they are:  words.Poor form, Virgil.  One hopes that you'd learn decorum, but, it's notyour style.So, readers, thank you for reading, I'm interested in yourconsiderations on the mathematical structures described here, andwould appreciate simply direct comment to a well-ordering of the realsseeing either a, or b (or some reasonable alternate):        a) nesting leaves an empty interval (set between two points ortwo copies of a point), and the mapping is onto, or        b) it doesn't, and there's an unmapped element to thesequenceRegards,Ross "Ernest" Finlayson
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