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

Am Wed, 09 Oct 2024 18:47:39 +0200 schrieb WM:

Am 09.10.2024 um 18:12 schrieb Alan Mackenzie:

WM <wolfgang.mueckenheim@tha.de> wrote:

 

You've misunderstood the nature of N.  The set is not {1, 2, 3, ...,
ω}, it is {1, 2, 3, ...}.

I use ℕ U {ω} for clarity.

This makes it clear that w-1, w-2 and so on are not included.

Should all places ω+2, ω+4, ω+6, ... remain empty?

It's not clear what you mean by this.  There are no such "places".

According to Cantor they are there in actual infinity.

What are these "places"?

Should the even numbers in spite of doubling remain below ω?

Yes, of course.

Then they must occupy places not existing before.

No.  Remember the set is infinite, so you cannot use finite intuition
to reason about it.

Numbers multiplied by 2 do not remain unchanged. That is not intuition
but mathematics.

They do, however, remain natural.

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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.