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Topic: Uncountable Diagonal Problem
Replies: 52   Last Post: Jan 6, 2013 2:43 PM

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 ross.finlayson@gmail.com Posts: 2,720 Registered: 2/15/09
Re: Uncountable Diagonal Problem
Posted: Dec 31, 2012 11:05 AM

On Dec 30, 9:48 pm, Virgil <vir...@ligriv.com> wrote:
> In article
>  "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
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

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