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

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.
This just shows the unusual behavior of infinite sets.

 

NO natural number when doubled results in a value that wasn't a natural number all the time.

 That may be, but then not all natural numbers have been doubled. There are larger natnumbers available.

Nope, we did the COMPLETE INFINITY, since we has that actual infinity to process.
If there are larger numbers, we never has the actual infinity you assuemd.
Thus proving that your concept of Actual Infinity, isn't actually infinite.
Which is why you get all the wrong answers, you assume that the actual infinity is finite and obeys the rules of finite set, because that is all you can think about.

 Regards, WM
 Regards, WM