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

On 12.10.2024 19:10, joes wrote:

Am Sat, 12 Oct 2024 15:32:25 +0200 schrieb WM:

On 10.10.2024 21:48, joes wrote:

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

>

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

They do, however, remain natural.

They do not remain the same set as before. They cover more of the real
line. If they all are natnumbers, then there are more than at the
outset. That means potential infinity. If there are not more natumbers
than at the outset, then infinite numbers have been created. There is no
way to avoid one of these results.

Of course multiplying a (finite) number by 2 changes the value.
If anything, the even numbers cover less, being a subset of the naturals.

2n > n. Every doubled number has twice the distance from zero.

If doubling a natural yielded omega, there would need to be an n = w/2.
That is not defined, nor finite.

If doubling does not yield an infinite number, then not all natnumbers had been doubled.
Regards, WM