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

On 11/4/24 12:11 PM, WM wrote:

On 04.11.2024 13:14, Richard Damon wrote:

On 11/4/24 6:07 AM, WM wrote:

 

By induction you can prove the sum n(n+1)/2 for every initial segment 1+2+3+...+n. But not for all natural numbers.

 

But all Natural Numbers can be defined.

 All defined numbers can be summed. Not all natural numbers can be summed.
 Regards, WM

Why not?
The Natural Numbers are exactly the set of Numbers defined by Zero, and the successor of some other Natural Number (where each number has just one successor), so all are defined, Every Natural Number is either Zero, or the successor of some other defined Natural Number.
The rules defining arithmatic on those Natural Numbers work on them all.
I guess you don't have a complete mathematics at your disposal.
Or maybe the problem is you can't have the full set of the Natural Numbers in your logic system, and that is causing your darkness.