Re: Simple enough for every reader?

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

On 30.05.2025 11:36, Mikko wrote:

On 2025-05-29 14:47:49 +0000, WM said:
 

It is in certain mathematical structures but not in all.

 Anyhow a reader in sci.logic should understand it.

 Everybody should understand at least arithmetic induction and its
limitations. But everybody doesn't.

 "Not everybody does" would be correct.

 Cantor did not use ℵo for infinity in general but only for a particular
kind of infinity.

 For all infinite sets of natural numbers he used it. That's what I discuss here.

Only after proving that all infinite subsetssets of the set of natural
numbers are equinumerous.

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.

 But P[n] -> P[n+1] is not there.
 

Do you doubt ℵo - 1 = ℵo?

 That can't be said in Peano arithmetic.

 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.
--
Mikko