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

On 10/22/24 4:05 AM, WM wrote:

On 21.10.2024 21:38, Chris M. Thomasson wrote:

On 10/21/2024 2:59 AM, WM wrote:

No set of numbers can include larger numbers.

>
What do you mean? Define a "large" number, say a natural one?

 No set of natural numbers can include *larger* numbers than it consists of. If the set is actually infinite, then all its numbers are there and can be doubled. Because of 2n > n larger numbers are created. If they are natural numbers they prove that the set originally was not complete because it did not contain the larger numbers.
 (In potential infinity this is not a problem because there is no completeness demanded).
 Regards, WM
  

But since the Natural Numbers are infinite, there isn't a "largest" element of the set, as it defines that every number has one that is larger than it.
So, you are just proving that what YOU call the Natural Numbers was not complete, as you stopped in the generation process before you completed it.
Thus, your statements are just based on lies.