Re: Simple enough for every reader?

On 26.05.2025 02:52, Ben Bacarisse wrote:

WM <wolfgang.mueckenheim@tha.de> writes:

With pleasure:
For every n ∈ ℕ that can be defined, i.e., ∀n ∈ ℕ_def:

 I can't comment on an argument that is based on a set you have not
defined.

Can you understand my proof by induction?
The resulting set is ℕ_def. (According to set theory however it is not a set but a potentially infinity collection.)

Your textbook defies N

It defines ℕ_def. All natural numbers reached by induction belong to ℕ_def. I did not distinguish it from the actually infinite set ℕ because my textbook does not consider actual infinity at all.
But if you understand my proof, then you see that not all natural numbers can be reached by induction. Almost all remain dark. That is clear even if you can't understand ℕ_def.
Regards, WM