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

Am Sat, 12 Oct 2024 18:51:10 +0200 schrieb WM:

On 10.10.2024 21:51, joes wrote:

Am Wed, 09 Oct 2024 15:24:21 +0200 schrieb WM:

On 09.10.2024 14:38, joes wrote:

Am Wed, 09 Oct 2024 10:11:20 +0200 schrieb WM:

There are no other end segments, none are finite.

They all have an infinite intersection.

Intersection with what?

Only the intersection of finitely many segments is infinite.

Of course. If infinitely many numbers are indices, then infinitely many
cannot be contents.

What? There's a segment for every number.

because 'infinite' DOES NOT mean 'very large'.

Theorem: If every endsegment has infinitely many numbers, then
infinitely many numbers are in all endsegments.

Invalid quantifier shift.

Valid quantifier shift.

You haven't proved your logical rule in general. In particular, you
can't use it here to argue it is valid, that would be circular.

The proof of the cake lies in the eating.
I do not intend to prove quantifier shift in general. I prove: If every
endsegment is infinite, then infinitely many numbers are in all
endsegments of this subset.

Then you need to explain why the shifted proposition should be true.

Can you explain what a quantifier shift is?

The above arguing. If every endsegment has an infinite subset, then
there exists one and the same infinite subset of every endsegment.
Proof: Inclusion monotony.

Not valid for infinite sets.

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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.