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

On 19.10.2024 22:19, Alan Mackenzie wrote:

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

The result covers twice the interval, ....

 It does not, except in the sense that twice infinite = infinite.

Twice the infinite contains numbers not in the first infinite. What else could twice mean?

 

.... containing numbers not in the original set ℕ.

 No.  If you think that, then give an example of a 2n which "isn't in the
original set N".

These numbers are dark. Their existence is proven by the fact that
∀n ∈ ℕ, n < 2n.

You won't and you can't.  But you'll likely come back
to your standard get-out clause about (non existent) "dark numbers".

The only alternative is that doubling numbers creates only doubled numbers. It is not acceptable. It cannot be apologized by the possibility to map all numbers on even numbers.
Regards, WM