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

On 08.10.2024 12:04, Alan Mackenzie wrote:

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

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.

Points either are or are not. The points that are include one point next to zero.

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.

Of course, the core is dark.

 The
"core" is thus empty.

The infinite sets contain what? No natural numbers? Natural numbers dancing around, sometimes being in a set, sometimes not? An empty intersection requires that the infinite sets have different elements.

 

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.

Shrinking sets which remain infinite have not lost all elements.

I understand it full well, and I understand that it's
mistaken.

Impossible. You don't understand that all sets are infinite and cannot have lost all elements.
Regards, WM