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

On 09.10.2024 14:26, joes wrote:

Am Wed, 09 Oct 2024 11:47:57 +0200 schrieb WM:

On 08.10.2024 21:23, joes wrote:

Am Tue, 08 Oct 2024 17:30:19 +0200 schrieb WM:

On 08.10.2024 15:26, joes wrote:

Am Tue, 08 Oct 2024 12:46:01 +0200 schrieb WM:

>

Because infinitely many natural numbers are contained. This is true
for all infinite sets of the function. Therefore they cannot have
lost all numbers.

What does „they” refer to in the last sentence?

All endsegments which have infinitely many natural numbers.

We are, again, not talking about an element of the sequence, which has
a natural index, contains infinitely many successors and is missing a
finite number of predecessors.

I am talking about such endsegments. Their intersection is infinite.

Such an intersection is itself part of the sequence.

Of course.

 

What we are talking about is the, pardon,
limit of whatever function.

The limit-endsegment is empty.

Why?

Because every n has become an index and then is lost.

The intersection is infinite because all infinite endsegments contain
the same infinite set. Some have lost more or less numbers but the core
remains infinite in all infinite endsegments.

And how many segments have been intersected?

(Potentially in-)finitely many because the collection of indices is finite as long as an infinite set of numbers remains within the endsegments.
Regards, WM