Re: Simple enough for every reader?

On 12.06.2025 09:56, Mikko wrote:

On 2025-06-11 11:30:26 +0000, WM said:

For all natural numbers that can be chosen as individuals:
|ℕ \ {1, 2, 3, ..., n}| = ℵo.
The "..." can be removed by the inductive proof
for all definable n ∈ ℕ:
|ℕ \ {1}| = ℵo.
|ℕ \ {m ∈ ℕ | m < n}| = ℵo
==> |ℕ \ {m ∈ ℕ | m < n+1}| = ℵo.

 That the set difference of an infinite set and a finite set is infinite
is well understood and therefore an uninteresting result.

That is not the only result. Interesting is that all defined numbers belong to a finite initial segment. Therefore most numbers are dark.

 

Result: It is impossible to define all natural numbers with none remaining undefined.

 You have not derived that "result".

I have shown it above by induction which you unfortunately cannot comprehend. Further it is well understood.
Regards, WM