Re: Contradiction of bijections as a measure for infinite sets

Le 25/03/2024 à 20:38, Jim Burns a écrit :

 for not.finiteⁿᵒᵗᐧᵂᴹ ℕ
exists 1.to.1.map ℕ∪{Bob} ⇉ ℕ

 A silly and wrong claim.
The infinite bijection ℕ <--> ℕ consists of infinitely many finite bijections. At least one of them must be destroyed when introducing Bob.

 You can add Bob to ℕ

Irrelevant. You cannot add a natural number to ℕ. But a bijection of ℕ with |E = {2, 4, 6, ...} would prove that both sets have the same number of elements. Adding an element to |E destroys this state and shows ℕ is larger than ℕ. Contradiction!
Regards, WM