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Re: Cantor's first proof in DETAILS
Posted:
Nov 26, 2012 1:48 AM
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On Nov 25, 9:37 pm, Virgil <vir...@ligriv.com> wrote:
> In article
> <87566fe7-ec39-46e1-b887-8200b2db8...@n2g2000pbp.googlegroups.com>,
> "Ross A. Finlayson" <ross.finlay...@gmail.com> wrote:
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> > On Nov 25, 6:16 pm, Virgil <vir...@ligriv.com> wrote:
> > > In article
> > > <bdf4255c-7c27-4c2b-a78c-62a2e38ec...@v6g2000pbb.googlegroups.com>,
> > > "Ross A. Finlayson" <ross.finlay...@gmail.com> wrote:
>
> > > > No, the conscientious mathematician doesn't just adhere to and
> > > > elaborate the mundane, but here acknowledges there is more to
> > > > mathematics than we yet have, and strives for truth, here mathematical
> > > > truth, as it is. As a follower of mathematics, Virgil is of the timid
> > > > sort, always using argument established by others, thus to lend
> > > > credence to his opinion regardless of his tactics, vis-a-vis,
> > > > establishing original thought, here of course in a framework of
> > > > mathematics.
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> > > A great majority of "original thought" is garbage, and must be filtered
> > > through what is already established in order separate out the dross.
> > > When one filters the dross out of Ross' "original thoughts" there is far
> > > to often nothing left at all.
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> > > > The conscientious mathematician doesn't just curate and dust.
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> > > But must curate and dust too!
> > > --
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> > Huh, that's not very funny.
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> Was not meant to be. Those who think that what haas gone before must
> always be replaced by new things, as Ross seems to, seams not to
> understand that culture, even in mathematics, advances by accumulation.
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> The mathematics of Euclid and Pythogoras is still of value even today,
> and those, like Ross, who would throw it out with their bathwater
> because it is not new, will lose it all.
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> > Virgil's opinion on original thought: "garbage". He claims to know
> > much about it.
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> New mathematics is fine as long as one does not have to throw out a
> couple of millennia of old math to use it.
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> > Get out of me and Cantor's way.
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> I agree with Cantor's mathematics but have yet to see anything by Ross
> that qualifies as math, old or new.
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> > EF, the equivalency function, is like no other function
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> Unlike actual functions, it is nonsense, not really a function at all.
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> I defy Ross to give his alleged "equivalency function" a mathematically
> acceptable definition of his alleged "equivalency function"here which
> demonstrates that it has either any equivalency or any functionality.
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> In the past he has never done more with it that a lot of bizarre hand
> waving and promises that it will square the circle and duplicate the
> cube.
> --
No, I certainly hold as right as you do all our ancient and modern
mathematics. And moreso, they were once new. Now, I'm not saying you
should throw me off the boat because of a claim that the square root
of two is irrational, which it is. No, there are true facts about the
objects of discourse in standard theory, and Goedel proved that there
are true facts of the objects beyond the standard, in standard theory,
in incompleteness.
In fact, a large part of the reason for development of a modern, post-
standard, theory of geometry, sets, and numbers, is to reach for the
applied that is beyond the standard, including the standard, as
applied, and conciliation, in the pure, in mathematics.
For example, the integral calculus, which is readily and often
applied, uses countable additivity. Real analysts would readily make
use of and incorporate as much mathematics as could be applied, here,
there's countable additivity that defines measure useful real measure,
in the standard, in real analysis. Constructively, modern real and
discrete analysis and all that follows in the applied can be read out
from asymptotics instead of the infinite. (Of course, don't get me
wrong, I believe in the infinite, else, for example, we'd be in finite
reference frames and motion would be classical.)
An aside could aver to results of Vitali and Banach-Tarski, and how
these "paradoxes" are examples of what were once "paradoxes".
No, by no means do my theories of geometry, numbers, and sets discard
mathematics, only extending mathematics. For example there is much
use of transfinite ordinals. Indeed, it is a goal of any erstwhile
mathematician to discover, to extend, mathematics.
EF is simple and it's defined simply as a function, not-a-real-
function, standardly modeled by real functions. Dirac's delta and
Heaviside's are as so defined, as functions, not-real-functions,
standardly modeled by real functions. And, the definition of function
itself, here is modern and reflects over time the development of the
definition of what is a mathematical function. Then, in actually
extending the definition of what are the real numbers, in A theory, it
is directly defined, and applied.
There are hundreds of essays on it here.
So, thank you I don't have much use for "bizarre hand-waving", instead
would rather certainly that all parties here ascribe to the same
highest ideals of mathematical logic. And no I've never claimed to
trisect the angle in finite constructions nor other circle-squaring
notions, though, of course, in the asymptotic, constructions trisect
the angle. Perhaps you're confused with some other poster you badger.
Not all who wander are lost.
An erstwhile mathematician's career is to discover to extend
mathematics. It's every grad student's dream to extend mathematics,
into the pure, applied, and concrete. I'm just lucky with a simple
right-place, right-time, confluence of events, then with carrying that
out: discovery, to extend mathematics.
That you think new mathematics would see "throw[ing] out a couple of
millenia of old math" is ridiculous.
Now, that's funny.
Regards,
Ross Finlayson
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