Re: Ultimate debunking of Cantor's Theory

On Jul 17, 5:30 am, WM <mueck...@xxxxxxxxxxxxxxxxx> wrote:
On 16 Jul., 23:36, MoeBlee <jazzm...@xxxxxxxxxxx> wrote:

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".

It is just that what can be proved without axioms, namely proved by
experiment.

You've not shown any "experiment" that "proves" that the set of real
numbers is countable.

The DEFINITION of 'function' does not require the terms 'domain' and
'range'.

Why then does a function require it?

What does "require" mean? Evey function HAS a domain, but the
DEFINITION of a function does not require mentioning that fact. As to
why every function "requires" a domain, the answer is in the proof
that every function (indeed, every set) has a domain!

Why don't you understand that?

Every commercially sold automobile has a vehicle number, but it is not
necessary to mention vehicle numbers to define 'commercially sold
automobile'.

What don't you understand about this?!

That for every function there is a unique domain and a unique
range of that function is, of course, a theorem of set theory

If a function is defined to have no domain, then nobody can prove that
it has a domain.

NO, a function is NOT defined to have no domain. A function is defined
to be a many-one relation. We do not say "x is a function iff such and
such and x has no domain."

Do you understand the difference between, on the one hand, not
requiring that we mention the domain of a function to form a
definition of 'is a function' and, on the other hand, requiring that
we say 'a function has no domain'?

I mean really, are you SERIOUS?

We don't require mentioning 'domain' just to define 'is a function',
but we don't thereby say that a function does not have a domain, and
we DO in fact prove that every function has a domain. It's just that
the definition of 'is a function' does not require mentioning that
proof that comes AFTER the definition.

MoeBlee

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