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

Am Thu, 10 Oct 2024 20:53:07 +0200 schrieb WM:

On 10.10.2024 20:45, Alan Mackenzie wrote:

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

 

If all natnumbers are there and if 2n is greater than n, then the
doubled numbers do not fit into ℕ.

For any finite n greater than zero, 2n is greater than n.  The same
does not hold for infinite n.

There are no infinite n = natural numbers.

Exactly! There are furthermore no infinite doubles of naturals (2n).

Numbers multiplied by 2 do not remain unchanged.

Either doubling
creates new natural numbers. Then not all have been doubled. Or all
have been doubled, then some products fall outside of ℕ.

No.  Not even close.

Deplorable. But note that all natural numbers are finite and follow this
law: When doubled then 2n > n. If a set of natural numbers is doubled,
then the results cover a larger set than before.

Additionally: if n is finite, so is 2n. It cannot go beyond w.

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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.