Re: Cantor Confusion

mueckenh@xxxxxxxxxxxxxxxxx wrote:
David Marcus schrieb:

Indeed. If people *object* to an axiom, that is philosophy.

But if people choose a set of axioms, that is what?

Everyone is welcome to choose their own axioms.

That's mathematics?

Of course.

And if people not decide to use an axiom, that is what?
But if people decide not to use an axiom, that is philosophy?

I said, "If people *object* to an axiom, that is philosophy." If you
want to see what theorems you can prove using a particular set of
axioms, that is mathematics. Whether your results will be interesting or
useful to other people is a different question.

Would like to do. Please le me know which words are available in your
universe of discourse.

I told you several times that the terminology in any modern textbook is
fine. For some reason you do not like this answer.

I told you the terminology used in a modern textbook to show that
finished infinity is used there. For some reason you do not like to
understand it.

"Some mathematicians object to the Axiom of Infinity on the grounds
that a collection of objects produced by an infinite process (such as
N) should not be treated as a finished entity."

Are you intentionally being stupid? That quote doesn't use "finished
infinity" nor does it give a definition of "finished entity". The quote
is simply a philosophical remark in a math textbook.

What would be something that is "actually infinite"?

Read Cantor, he can explain it better than me.

Hah! So, you can't give an example. Then please stop using the words!

e. An "infinite number" is a number other than the natural numbers.

An "infinite number" would be a number other than a natural number.

Are you agreeing or disagreeing?

I am astonished that you cannot understand simplest sentences.

I only seem to have this "problem" with your sentences.

I asked whether you agreed with a statement and you replied by offering
a different statement. Do you disagree with the original or agree?

You seem
to have difficulties with conditional constructs. Should you ever
intend to study mathematics be prepared that such constructs will
appear quite frequently.

How would you know such constructs appear frequently if someone studies
mathematics? What mathematics have you studied? Where did you study it?
Do you have a doctorate in Mathematics? Who was your thesis advisor?
Have you published any articles in refereed mathematics journals?

If an actually infinite set of numbers existed, and if neighbouring
elements had a fixed distance from each other, then the set must
contain an infinite number.

Is that a "no" or a "yes"?

Read again, simplified: If neighbouring elements have a fixed distance,
the answer is yes.
If neighbouring elements have not a fixed distance like the rational
numbers: the answer is no

Let's try a simpler question:

Does an actually infinite set exist?

--
David Marcus
.

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