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

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

On 07.10.2024 14:11, Alan Mackenzie wrote:

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

You have not understood that all unit fractions are separate points on
the positive axis.

I understand that full well.

Then you understand that every point, if existing, is independent of the
others.

Not sure what you mean by "independent of" here.  Each point exists.

All unit fractions are points with uncounably many points between each
pair.

Yes, OK.

Hence all must be visible including the point next to zero, but they
are not.

There is no point next to zero.  All rationals are points with
uncountably many points between each pair.  That includes between zero
and any other rational, including a unit fraction.  There is no "next
to", here.

A shrinking infinite set which remains infinite has an infinite core.

Again, no.  There is no such thing as a "core", here.  Each of these sets
has an infinitude of elements.  No element is in all of these sets.

Try to think better. A function of sets which are losing some elements
but remain infinite, have the same infinite core.

That is untrue.  For any element which you assert is in the "core", I
can give one of these sets which does not contain that element.  The
"core" is thus empty.

That argument is absolutely definite, a logical necessity. If you
cannot understand it, ....

It wasn't an argument, it was a bare statement, devoid of any supporting
argument.  I understand it full well, and I understand that it's
mistaken.

.... then it is useless to continue this discussion.

Maybe that is the case.

Regards, WM

--
Alan Mackenzie (Nuremberg, Germany).