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

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.

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.

 

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.

 

That means the original set had not contained all natural numbers. That
mans no actual or complete infinity.

 Nonsense.

Sorry, you are a real believer but cannot discuss rational arguments.
Regards, WM