Re: An uncountable countable set

On 20 Oct 2006 13:39:32 -0700, "MoeBlee" <jazzmobe@xxxxxxxxxxx> wrote:

MoeBlee wrote:
Tony Orlow wrote:
I'm reading Non-Standard Analysis instead.

What book?

You really would be better served by having your basics in set theory
and mathematical logic in order first and then taking on non-standard
analysis.

Robinson agrees there's no
smallest infinity,

Then that is not the same as the ordering of the ordinals we're talking
about. I very much doubt that Robinson claims that there is not a least
infinite ordinal.

Please tell me exactly what passages or theorems you are referring to
in Robinson's work so that I can see exactly what it is you are talking
about.

And this reminds me that you never did come to understand the
difference between cardinality and ordering. I and others have pointed
out to you that you conflate these. One doesn't even need non-standard
analysis to provide an ordering in which there is a set S with no least
member yet with every member of S greater than some set with no
greatest member. But that ordering is not an ordering by cardinality.
Yes, PA has models in which there are different orderings so that
objects are called 'infinite' per these orderings, but this is NOT the
same sense of 'infinite' as that of the cardinality sense. And we can
define a division operation on these "infinite" objects to get
infinitesimals, but again, this is not the same as cardinality.

Moreover, you must be very careful to distinguish between the proof of
the existence of certain models and a RECURSIVE axiomatization for a
theory of which the model is a model of.

Ah another lecture in neomathspeak. See the problem is that Tony just
doesn't agree with you. And there is nothing in what you say which can
bridge that gap because nothing in the orthodox catechism of standard
set methodology (I'm assuming it's standard) can be demonstrated true.
You and he just have different perspectives on the problem and nothing
in what you have to say has any relevance to what Tony believes any
more than what Tony believes has any relevance to what you believe.
Which is undoubtedly why he has begun to study non standard analysis
before satisfying your criteria for the standard set methodologies you
believe in. And though your beliefs are pervasive, to the extent they
aren't demonstrably true your arguments are irrelevant because they're
unable to effect a suspension of disbelief in Tony. In general terms
it's called a crisis of faith.

~v~~
.

Relevant Pages

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