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

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

On 15.10.2024 00:27, Chris M. Thomasson wrote:
 

Take the index, using natural numbers
>
1: { 1 }
2: { 1, 2 }
3: { 1, 2, 3 }
4: { 1, 2, 3, 4 }
...
>
vs:
>
1: { 2 }
2: { 2, 4 }
3: { 2, 4, 6 }
4: { 2, 4, 6, 8 }
...
>

There is a general rule not open to further discussion:
When doubling natural numbers we obtain natural 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.
 Regards, WM
 

But that isn't actually a general rule, so you are just admitting that you aren't talking about the same Natural Numbers that everyone else is talking about, but some bastardization that is just finite.
NO natural number when doubled results in a value that wasn't a natural number all the time.
Your problem is that your "Acutal Infinity" isn't actually Infinity, and like isn't actually "actually".