Re: counter example in analysis

In article <455879AC.2060501@xxxxxxxxxxxxxxxxxxx>,
Eckard Blumschein <blumschein@xxxxxxxxxxxxxxxxxxx> wrote:

On 11/8/2006 9:06 PM, Virgil wrote:


In Cantor's understanding all rational and even all real numbers exist.

And Eckard sets himself up as knowing better, while clearly ignorant of
the mathematical basis for Cantor's work.

I read Cantor's original papers. His basis is just intuitive guesswork.

His "guesses" have been confirmed.


This is however shallow reasoning because there is no limit (except such
phantasm like omega) to the rationals.

All numbers are equally phantasms.

This deliberately misleading claim does not differentiate between
countable genuine numbers and uncountable fictions.

It does not differentiate between countable fictions and uncountable
fictions, since numbers are all equally fictitious, made uo things with
no physical existence. They are creatures of imagination, and as such
are all equally imaginary, having no ore reality than unicorns or
basilisks.


Any singleton set is countable and any finite set is countable in the
mathematical meaning of the word.
Eckard's use of "countable" and "uncountable" is unaccountable.

An element of a set can itself be a set. If you will accept this idea
then you ought to also accept that single "numbers" like pi may be
uncountable ones.

So that EB is claiming that the number of elements in a set with one
member may be uncountable? Not in any consistent set theory.

When one speaks of a set being countable, on is talking about how many
members it has, not the nature of those members.

I spoke of countable and uncountable numbers, not sets. If pi is a
number at all, then it is an uncountable one. Neither does it fit into
the system of rational numbers, nor can it be expressed numerically with
any finite number of steps.

But pi is a set, as are all real numbers, in both the Dedekind model and
the Cauchy model. What model of reals does EB propose in which reals are
not sets?


A set with one member is a countable set with one member no matter how
large that member may be as a set.

This is correct but distracting.

It certainly distracts from EB's idiocy, which is a benefit, rather than
a fault.


Eckard should get his head straight about such simple matters before
pontificating.

Pontificating on what? I always try to explain what I mean.

You "explain" what your dogma says, which is pontificating.

Most of us have the wit to see that you are not actually speaking ex
cathedra.
.

Relevant Pages

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