1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook