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

On 9/9/24 2:44 PM, WM wrote:

On 09.09.2024 17:15, joes wrote:
 

I still don’t understand. You can choose any size of interval and slide
it around to include an arbitrary number of unit fractions.
>

ℵo unit fractions exist invariably and require a minimum length d. Take one of the ℵo gaps. It is smaller than d.

A GIVEN infinte set of unit fractions will have a total. length of d, but by just removing a finite number of the largest elements, you still have an infinite set, and the size of that new set can be made as small as you want (as long as that value is actually > 0)
You don't seem to understand this fact, and think you are stuck with just one infinite set.

 Simplest argument: If a chain of real points exists on the real axis, then it has a beginning.

Which is a FALSE statement when about infinite sets. Infinite sets might not have a "beginning" in the set.

 Regards, WM