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

 Messages: [ Previous | Next ]
 ross.finlayson@gmail.com Posts: 2,720 Registered: 2/15/09
Re: Uncountable Diagonal Problem
Posted: Dec 31, 2012 10:21 PM

On Dec 31, 1:18 pm, Virgil <vir...@ligriv.com> wrote:
> In article
>  "Ross A. Finlayson" <ross.finlay...@gmail.com> wrote:
>
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> > On Dec 30, 9:58 pm, Virgil <vir...@ligriv.com> wrote:
> > > In article
> > >  "Ross A. Finlayson" <ross.finlay...@gmail.com> wrote:

>
> > > > This is from that, the constructed sequences (here ordinally-valued)
> > > > of nesting endpoints, of an interval, either meet or don't.

>
> > > In comprehensible!
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> > > Why is it that Ross' attempts at expression himself about things
> > > mathematical are always more obfuscating than clarifying?

>
> > > The rest is silence!
> > > --

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> >http://en.wikipedia.org/wiki/The_Oak_and_the_Reed
>
> But Ross is, as yet, no more than an acorn.
> --

Ah, that's rich. It's a rather poor metaphor, but how low you'll
stoop for it is notable.

Unless you've discovered some way to blank the memory of others, there
are quite a few who could recount the salient points from memory, at
least of the definition of what the E.F. or EF is, whether or not they
would care to defend it or discount it. And, even though you've
displayed of yourself a lack of memory, I wouldn't so ascribe that
lack thereof to others.

I see you won't quite comprehend, a scene of a battle of wits:
http://princessbride.8m.com/script.htm#19 .

Good luck with that.

So, in the well-ordering of the reals, for any initial segment, as
defined by an ordinal, where the well-ordering is a function from the
ordinals onto the reals, in the course-of-passage there is a
concomitant interval defined by the elements of the reals in their
well-order. These intervals, nested in the previous, see that the
endpoints converge. Do they meet? If they don't, the interval is non-
empty, and there's not an element of the reals there, eventually in
order. If they do meet, where there are no points within the
interval, they are consecutive, or duplicate.

You could well note that the interval endpoints converge to each
other, in the countably infinite. The endpoints meet: or don't.
Cantor's first has their intersection: non-empty.

http://en.wikipedia.org/wiki/Cantor%27s_first_uncountability_proof

So, do they: do, or don't?

Maybe it's as simple as that any well-ordering of the reals, contains
duplicates. Would that not be a surprising concomitant fact? Yet,
then only note to nest the unique ones.

Well-order the reals. While you're at it: count the integers.

Regards,

Ross Finlayson