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Math Help - Proof of invertibility of injective functions

  1. #1
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    Proof of invertibility of injective functions

    Would someone please help me with construction of a proof that every invertible function is injection.

    Thank you.
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Re: Proof of invertibility of injective functions

    Quote Originally Posted by itpro View Post
    Would someone please help me with construction of a proof that every invertible function is injection.
    If f:A\to B is invertible, there exists g:B\to A such that g\circ f =I_A . Now,

    f(x_1)=f(x_2)\Rightarrow g[f(x_1)]=g[f(x_2)]\Rightarrow

    (g\circ f)(x_1)=(g\circ f)(x_2)\Rightarrow I_A(x_1)=I_A(x_2)\Rightarrow x_1=x_2
    Last edited by FernandoRevilla; December 31st 2011 at 12:45 AM.
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