Re: A flaw with Venkat Reddy's arithmetic.
- From: Jonathan Hoyle <jonhoyle@xxxxxxx>
- Date: Wed, 28 Nov 2007 15:20:06 -0800 (PST)
On Nov 25, 11:18 pm, "Ross A. Finlayson" <r...@xxxxxxxxxxxxxxx> wrote:
I don't want to be called a crank just for promoting post-Cantorian
theories of the infinite, non-well-founded set theories, and
nonstandard analysis.
You would not be called a crank for the last two of the three items
you mentioned. You would for the first, since the term "post-
Cantorian" is a codeword you use to describe crankish ideas.
I think infinity is post-Cantorian because the universe is infinite
realizing a counterexample to the powerset result, ZF contains itself
as a set theory and is thus non-well-founded, and in analysis with for
example the mutual density of the rationals and irrationals in the
reals there is a different consideration than that they are not
equivalent.
As we've discussed before, this run on sentence is filled with
nonsense. there is no "counterexample to the power set result", ZF is
a theory and thus cannot "contain itself", ZF is certainly well-
founded (although there are theories which are not), and on and on.
I'd find it unfortunate if that means being called a crank because I
see it as true.
Seeing nonsense as true is only one aspect of being called a crank,
but it takes much more. For example, when given a demonstration of
why your "proofs" are false, you simply ignore it rather than respond
and learn from it.
(I see the null axiom theory with ubiquitous naturals
representing the only possible consistent, complete, concrete: true
theory.)
A great example: you claim to generate theorems without axioms. When
challenged to demonstrate how, you create some fiction which is little
more than the mathematical equivalent to a bad pun. This is an
excellent example of why you are called a crank.
Consider for example the notion of the "infinitesimal". Now, there is
a resurgence in the usage of the term in education and practice,
because the objects under consideration don't not have the properties
of being infinitesimal objects. Thus, they are.
??? Thus, *what* are what?
Similarly here on sci.math there are notions along the lines of half
of the integers being even, a proper subset being smaller than a
superset, and etcetera that were once browbeaten as not truisms
and now aren't.
Of course they still are. Why do you think they are not?
There are infinitesimals somewhere, seemingly among the real numbers
(which are complete).
Incorrect. No real (other than 0) is an infinitesimal, which can
easily be proven. It is also provable that any extension of the reals
makes them incomplete. There are a number of different theories
incorporating infinitesimals, and I delivered a talk on five such
theories a couple of months ago at a recent Mathematical Association
of America meeting. If you are interested in what I spoke on, visit:
http://www.jonhoyle.com/MAAseaway/
Hope that helps.
Regards,
Jonathan Hoyle
http://www.jonhoyle.com
.
- References:
- A flaw with Venkat Reddy's arithmetic.
- From: mike3
- Re: A flaw with Venkat Reddy's arithmetic.
- From: G.E. Ivey
- Re: A flaw with Venkat Reddy's arithmetic.
- From: lwalke3
- Re: A flaw with Venkat Reddy's arithmetic.
- From: Ross A. Finlayson
- A flaw with Venkat Reddy's arithmetic.
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