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

Am Wed, 09 Oct 2024 15:35:10 +0200 schrieb WM:

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.

All endsegments are infinite.

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

All endsegments which have infinitely many natural numbers.

There are no others.

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.

Which intersection?

Such an intersection is itself part of the sequence.

Of course.

What about the intersection of all infinitely many segments?

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.

It is impossible to use up an infinity.

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.

No. You seem to imagine them as finite but sharing a mysterious omega.
Instead, replace that with "..." and you got it.

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.

And what if we intersect infinitely many?

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Am Sat, 20 Jul 2024 12:35:31 +0000 schrieb WM in sci.math:
It is not guaranteed that n+1 exists for every n.