Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary)

WM <wolfgang.mueckenheim@tha.de> wrote:

On 07.10.2024 18:11, Alan Mackenzie wrote:

What I should have
written (WM please take note) is:

The idea of one countably infinite set being "bigger" than another
countably infinite set is simply nonsense.

The idea is supported by the fact that set A as a superset of set B is
bigger than B.

What do you mean by "bigger" as applied to two infinite sets when one of
them is not a subset of the other?

The standard definition for infinite (or finite) sets being the same
size is the existence of a 1-1 correspondence between them.

You seem to be rejecting that definition.  What would you replace it by?
You have specified "bigger" for a special case.  What is your definition
for the general case?

Simply nonsense is the claim that there are as many algebraic numbers
as prime numbers.

It is not nonsense.  The prime numbers can be put into 1-1
correspondence with the algebraic numbers, therefore there are exactly
as many of each.  Again, if you mean something else by "as many", then
perhaps you could state what you mean.

For Cantor's enumeration of all fractions I have given a simple
disproof.

Your "proofs" tend to be nonsense.

Regards, WM

--
Alan Mackenzie (Nuremberg, Germany).