EDB — 1WS

[1WS]Let \(f:ℕ→ℕ\) be an assigned function and \(I\) its image, prove that \(A⊆ ℕ\) exists such that \(f|_{A}\) is injective and \(f(A)=I\). (Hint it may be useful to know that the usual order of \(ℕ\) is a well-order cf [07R]↺↻ and [26Y]↺↻).

Note: The result is true for any function \(f:A→ B\), but the proof requires the axiom of choice.