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Homework Help: How to prove that the composition of injection is an injection?

  1. Aug 5, 2010 #1
    how to prove it please?
     
  2. jcsd
  3. Aug 6, 2010 #2

    HallsofIvy

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    F(x) is "injective" if and only if f(x)= f(y) implies x= y.

    Suppose both f(x) and g(x) are injective and F= f(g(x))

    If F(x)= F(y) then f(g(x))= f(g(y)) so, since f is injective, we have g(x)= g(y). Now, since g is injective, ...
     
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