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E84

[2BZ]Prerequisites:[2BX].Consider the Zermelo-Fraenkel set theory, and this statement:

Given any \(A,B\) non-empty sets such that there exists a surjective function \(g:B→ A\), then there exists an injective function \(f:A→ B\) such that \(g◦ f=\text{Id}_ A\).

Prove that this statement implies the Axiom of Choice.

Solution 1

[2C0]

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Authors: "Mennucci , Andrea C. G." .
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  • left inverse
  • function, left inverse
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