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 equivalency function, N/U E F, may as well be called NUE, NUE(n), or EF.
E -> F, Empty -> Full
I dispute that Hancher - as do others who find the deliberations interesting - and mathematical - again your blathering caws serve nothing but to demean the discourse. We already have the edifice of modern mathematics for ready reference, again your ad hominem attacks have no place in a mathematical discussion, on mathematics, and the reader easily finds them as they are: words.
Poor form, Virgil. One hopes that you'd learn decorum, but, it's not your style.
So, readers, thank you for reading, I'm interested in your considerations on the mathematical structures described here, and would appreciate simply direct comment to a well-ordering of the reals seeing either a, or b (or some reasonable alternate): a) nesting leaves an empty interval (set between two points or two copies of a point), and the mapping is onto, or b) it doesn't, and there's an unmapped element to the sequence