Re: Ultimate debunking of Cantor's Theory

On Jul 16, 10:26 am, WM <mueck...@xxxxxxxxxxxxxxxxx> wrote:
On 16 Jul., 18:24, MoeBlee <jazzm...@xxxxxxxxxxx> wrote:

On Jul 13, 1:19 pm, WM <mueck...@xxxxxxxxxxxxxxxxx> wrote:

On 11 Jul., 16:28, tommy1729 <tommy1...@xxxxxxxxx> wrote:
another strange thing is that Cantor is not neccesary to perform math at all.

Correct.

It depends on what you mean by "perform math". Z set theories
axiomatize ordinary working mathematics. Any other proposal to
axiomatize ordinary working mathematics but without infinite sets is
also subject to evaluation for certain criteria such as prospect for
consistency, intuitiveness, naturalness, simplicity, ease of
application, scope, etc.

As I understand, there are various proposed formal axiomatizations

True mathematics needs no formal and no informal axiomatization. The
reason is that true mathematics is not arbitrary. For instance sinx/x
= 1 for x = 0.

Of course, you have your own definition of "true mathematics". And, of
course, if one is not interested in formal axiomatized theories, then
one can do whatever one's mathematical conscience allows. However, IF
one is interested in formal axiomatized theories (or even informally
axiomatized theories) then any such axiomatization is subject to
evaluation on a number of criteria.

In particular you should agree because you deny that a
function requires domain and range.

The DEFINITION of 'function' does not require the terms 'domain' and
'range'. That for every function there is a unique domain and a unique
range of that function is, of course, a theorem of set theory (indeed,
not just for functions, but for sets in general, given suitablly
common set theoretic definitions of 'domain' and 'range'). I don't
know why you don't understand that distinction between a definition of
a term and theorems that are proven after that definition.

MoeBlee


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