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

Am Mon, 09 Sep 2024 17:26:12 +0200 schrieb WM:

On 09.09.2024 17:14, joes wrote:

Am Mon, 09 Sep 2024 17:01:35 +0200 schrieb WM:

 

They all are present from the start. I simply choose a gap that is too
small to contain ℵo unit fractions.

How do you do that?

I know that all exist.

All unit fractions? How do you choose that interval?

How can a claim a set of values less then a SPECIFIC NUMBER if I
don't have the number?

I claim that all unit fractions are existing as real points of the
real line. Therefore there is a first one. NUF(x) cannot increase
without passing 1 when real points are counted. Your ℵo points cannot
exist without including 1, 2, 3 first points.

Those first points are on the right, obviously.

If ℵo points are there, then one is on the left-hand side.

Why should that be so? It is contradicted by the infinity of unit
fractions, and there is clearly an end on the right, and you can
step to the left, so there can’t be an end (other than a limit).

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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.