Results 1 to 2 of 2

Thread: Proof of invertibility of injective functions

  1. #1
    Newbie
    Joined
    Sep 2010
    Posts
    19

    Proof of invertibility of injective functions

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

    Thank you.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor FernandoRevilla's Avatar
    Joined
    Nov 2010
    From
    Madrid, Spain
    Posts
    2,163
    Thanks
    46

    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 $\displaystyle f:A\to B$ is invertible, there exists $\displaystyle g:B\to A$ such that $\displaystyle g\circ f =I_A$ . Now,

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

    $\displaystyle (g\circ f)(x_1)=(g\circ f)(x_2)\Rightarrow I_A(x_1)=I_A(x_2)\Rightarrow x_1=x_2$
    Last edited by FernandoRevilla; Dec 30th 2011 at 11:45 PM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Matrix proof involving invertibility and bases
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: Mar 23rd 2010, 08:14 PM
  2. Invertibility Proof
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: Nov 26th 2009, 08:48 AM
  3. injective functions
    Posted in the Differential Geometry Forum
    Replies: 5
    Last Post: Nov 21st 2009, 11:34 AM
  4. Injective functions
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: Nov 19th 2009, 05:05 PM
  5. Injective Functions
    Posted in the Calculus Forum
    Replies: 1
    Last Post: Nov 24th 2007, 12:53 AM

/mathhelpforum @mathhelpforum