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

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

On 19.10.2024 19:32, Alan Mackenzie wrote:

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

When multiplying all natural numbers by 2, then the number of numbers
remains the same but the density is reduced and therefore the interval
is doubled.

That's not mathematics.

It is mathematics.

It's merely your intuition, derived from finite sets and misapplied to
infinite sets.

It is the basic mathematics of natural numbers: 2n > n.

Of course 2n > n for all n > 0.  That has no connection with the other
crazy things you've been asserting.

If you believe in a different version of mathematics, try to find
people who are interested in that version.  I am not.

The other posters on this newsgroups, they are not hard to find.  We all
understand standard mathematics.  You do not.

In mathematics, there is no meaningful distinction between what you think
of as two different forms of infinity.

You have not the faintest idea of infinity.

But I do.  An infinite set is one which has a proper subset which can be
put into 1-1 correspondence with the original set.  That is the
definition.  You clearly don't understand that definition, and you go to
great lengths to preserve that lack of understanding.

Regards, WM

--
Alan Mackenzie (Nuremberg, Germany).