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Math Help - Proof using functions

  1. #1
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    Proof using functions

    Let f: A --> B be a function, and suppose that
    there is a function g: B --> A such that g circle f is
    the identity map on the set A. Prove that f is injective.
    (There is a very short proof.)
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  2. #2
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    Quote Originally Posted by brudman View Post
    Let f: A --> B be a function, and suppose that
    there is a function g: B --> A such that g circle f is
    the identity map on the set A. Prove that f is injective.
    (There is a very short proof.)
    Is this true f(a) = f(b)\, \Rightarrow \,g \circ f(a) = g \circ f(b)?
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