Re: Simple enough for every reader?

On 31.05.2025 11:59, Mikko wrote:

On 2025-05-30 14:25:22 +0000, WM said:

Here I use induction in Cantor's set. That is allowed. Cantor did it too.

 No, there is no artithmetic induction and no set induction there.

"daß die Reihe
1, i2, i3, ..., i, ...
nur eine Permutation der Reihe
1, 2, 3, ..., , ...
ist. Dies beweisen wir durch vollständige Induktion,"
[Cantor, collected works, p. 305]
All natural numbers of Peano's set, i.e., all definable natural numbers obey arithmetic induction:
P[n]: {1, 2, 3, ..., n} has infinitely many (ℵo) successors.
P[n+1]: {1, 2, 3, ..., n, n+1} has infinitely many (ℵo) successors.
For all ℵo - 1 = ℵo.
Regards, WM