EDB — 04G

[04G] Prerequisites:[08Z]↺↻.

A set \(A\) is called Dedekind–infinite if \(A\) is in bijection with a proper subset, that is if there is \(B⊂ A, B≠ A\) and \(h:A→ B\) bijection. Show that a set \(A\) is Dedekind–infinite if and only if there is an injective function \(g:ℕ→ A\). (This result does not require the axiom of choice.)