Re: Simple enough for every reader?

On 06.06.2025 09:37, Mikko wrote:

On 2025-06-05 20:36:45 +0000, WM said:
 

On 05.06.2025 09:32, Mikko wrote:

On 2025-06-04 17:32:28 +0000, WM said:

The expression "subtracting them individually" should be represented
mathematically, e.g. a sequence. Informal expressions tend to lead
to bad proofs.

>
This expression is represented by
>
((((ℕ \ {1}) \ {2}) \ {3}) ...) = { }

 That may be good enough when you want to prove something that we already
believe anyway. But for a sufficiently rigorous proof of something else
the "..." should be replaced with something more mathematicsl.

The "..." can be replaced with the singletons of definable natural numbers but the result is not the empty set. It is impossible however to replace them with the singletons of all natural numbers in order to make the result true. Just this is the proof that not all natural numbers are definable.
Regards, WM