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Re: Uncountable Diagonal Problem
Posted:
Dec 31, 2012 11:05 AM
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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
Regards,
Ross "Ernest" Finlayson
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