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

On 17.10.2024 02:18, Richard Damon wrote:

On 10/16/24 11:20 AM, WM wrote:

On 16.10.2024 13:54, Richard Damon wrote:

On 10/16/24 4:30 AM, WM wrote:

>

There is a general rule not open to further discussion:
When doubling natural numbers we obtain even numbers which have not been doubled.
In potential infinity we obtain more even natural numbers than have been doubled.
In actual infinity we double ℕ and obtain neither ℕ or a subset of ℕ.
>

But that isn't actually a general rule,

>
It is a general rule that doubling creates larger numbers.

 Yes, but none get larger than the domain of the Natural Numbers, the set we started from.

When doubling natural numbers we obtain even numbers which have not been doubled.

This just shows the unusual behavior of infinite sets.

2n > n is always true, in finite and in infinite sets.

 you assume that the actual infinity is finite

No, it is simply complete. Therefore not for all n 2n can be a natnumber.
Regards, WM