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Re: The Distinguishability argument of the Reals.
Posted:
Jan 7, 2013 12:31 AM
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On Jan 6, 7:18 pm, Virgil <vir...@ligriv.com> wrote:
> In article
> <c0440244-4535-4b3f-8e2d-52e086b7c...@lb9g2000pbb.googlegroups.com>,
> "Ross A. Finlayson" <ross.finlay...@gmail.com> wrote:
>
> > > For each value of d, the range is a finite subset of d+1 values in [0,1].
> > > You may properly may say that the codomain for each d is [0,1], but the
> > > range is the set of values values actual taken by the function, and for
> > > each value of d the range is a set of d+1 values, not an interval.
>
> > > Wrong again, Ross!
> > > --
>
> > Ah, that's (partly) fair
>
> That's totally fair.
>
> Garbage snipped.
> --
Meh. (General spiel at Virgil's expense omitted, though I readily
produce them.)
Apocryphally: "But what is much more widespread than the actual
stupidity is the playing stupid, turning off your ear, not listening,
not seeing."
"Joy in looking and comprehending is nature's most beautiful gift."
"A theory is the more impressive the greater the simplicity of its
premises is, the more different kinds of things it relates, and the
more extended is its area of applicability."
-- http://en.wikiquote.org/wiki/Albert_Einstein
Thanks, Einstein.
Well readers I thank you for this chance to soapbox these notions of
novel treatments of the reals. And yes, I am interested in any
mathematical fault of mine. And, I'm more interested in developments
in foundations for novel applications, and sublime facts about our
numbers.
So, we know from Goedel's theorems of incompleteness that there are
already true things about these objects of our domain of discourse,
not theorems of the regular axiomatization, that would be mathematical
fact, and as so would direct our course in physics. ZF's universe in
a naive set theory contains itself, as does the Universe, as
mathematical, or set. The closer we find atoms in reality the smaller
they are found, the farther we look the more there is. The
infinitesimal, and infinite, does have a place not just in our lofty
esteem but as the abstract of our concrete. And, there yet remains to
be found what that is, in mathematics.
Then for the infinitely many real numbers from the origin, for the
beginning, that's: The End.
Then, warm regards,
Ross Finlayson
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