Re: how to list all of the real numbers

On Aug 9, 4:40 pm, lwal...@xxxxxxxxx wrote:

No, not everyone who thinks Cantor is not the end-all be-all when it
comes to infinity is a crank.

But standard mathematicians, of course, believe otherwise.

What is it you're saying that people who work in classical
("standard") mathematics believe about Cantor and cranks?

I agree that infinitesimals are possible, but unfortunately most
mathematicians will only consider standard theories.

Lots of mathematicians work in areas of specialty in which
infinitesimals are not relevent to their particular research. However,
just about anyone who works in foundations, including mathematicians
who work primarily in classical mathematics, knows about non-standard
models and of IST and of infinitesimal calculus on such bases. In
fact, non-standard models that provide for infinitesimal calculus are
PART of classical mathematics in the very sense that the existence of
non-standard models that provide for infinitesimal calculus is indeed
a theorem of ZFC and discussion of the matter is often even presented
in introductory textbooks in mathematical logic. Indeed non-standard
analyis is the result of a "stanadard" mathematician whose very GOAL
was to develop infinitesimal calculus within classical mathematical
logic.

You keep saying things about "most mathematicians" and "standard
mathematicians" but you don't seem to be aware of the actual
literature of the subject or even that ordinary mathematical logic
presents non-standard analysis even as an INTRODUCTORY part of the
subject.

MoeBlee


.

Relevant Pages

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    (sci.math)
  • Re: Another Inconvenient Truth
    ... One topic that comes up frequently in set theory threads here in this ... The standard mathematicians reply by stating that it is still possible ... the Axiom of Infinity is not in the existence of infinitely many ...
    (sci.math)
  • Re: A consideration concerning the diagonal argument of G. Cantor
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  • Re: Zenkins paper on Cantor (reply of Dr. Zenkin)
    ... > I wish to proceed with my studies of mathematical philosophy. ... fail the test of being about whatever it is that _mathematicians_ ... > proofs which do not necessarily use infinitary reasoning. ... > of actual infinity" is precisely enough, because we do not really know ...
    (comp.theory)
  • Re: Zenkins paper on Cantor (reply of Dr. Zenkin)
    ... > I wish to proceed with my studies of mathematical philosophy. ... fail the test of being about whatever it is that _mathematicians_ ... > proofs which do not necessarily use infinitary reasoning. ... > of actual infinity" is precisely enough, because we do not really know ...
    (sci.math)