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

On 07.10.2024 11:38, FromTheRafters wrote:

WM wrote :

On 06.10.2024 18:48, Alan Mackenzie wrote:

>

You are getting confused with quantifiers, here.  For each such x, there
is an infinite set of fractions less than x.  For different x's that set
varies.  There is no such infinite set which appears before every x > 0.

>
The set varies but infinitely many elements remain the same. A shrinking infinite set which remains infinite has an infinite core.

 Wow, your shrinking sets again? Sets don't change.

>
There is a set-function, a set of sets. Every x that is closer to zero makes the set smaller, but never finite. Therefore the argument that the set varies but does not keep the same infinite core is stupid.