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Help for a sets/functions theorem proof

  1. Oct 6, 2012 #1
    I am stuck at a proof and do not even have an idea where to start and how to start:

    Let X and Y be sets, and let f : X → Y be a surjection. Prove that there is an injection g : Y → X such that f (g(y)) = y for every y ∈ Y.

    Could you please show me a way?
  2. jcsd
  3. Oct 7, 2012 #2


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    Hint: you will need to use the axiom of choice to define g. For each y in Y, you need to choose an x such that f(x) = y.
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