Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

I Injective & Surjective Proofs

  1. Mar 8, 2017 #1
    Stumped on a couple of questions, if anyone could help!

    In what follows I will denote the identity function; i.e. I(x) = x for all x ∈ R.
    (a) Show that a function f is surjective if and only if there exists a function g such that f ◦ g = I.
    (b) Show that a function f is injective if and only if there exists a function h such that h ◦ f = I.
    (c) Suppose f ◦ g = I and h ◦ f = I. Show that g = h
  2. jcsd
  3. Mar 8, 2017 #2


    User Avatar
    Staff Emeritus
    Science Advisor

    Let's take one question at a time.

    For question (a), do the following exercise:

    1. Write down (in English, or using logical notation, if you know logic) what does it mean to say that a function [itex]f(x)[/itex] from one set, [itex]A[/itex] to another set, [itex]B[/itex] is surjective.
    2. Now, write down what it means to have a function from [itex]B[/itex] to [itex]A[/itex].
    3. Now, see if you can see any relationship between those two definitions.
    Post your answers to 1&2. The rules for Physics Forums is that you have to show your effort in order to get help.
  4. Mar 8, 2017 #3
    Ahh thank you for the pointer! First time posting so will keep that in mind. Will post my working out so far in the morning, also will repost this in the homework type question forum as I just read that these types of questions are best directed there.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted

Similar Threads - Injective Surjective Proofs Date
A Proof of Seifert-Van Kampen Theorem Oct 14, 2017
I Proof that retract of Hausdorff space is closed Oct 8, 2017
Existence of surjective linear operator Sep 8, 2014
Proving a known proof involving injection. Sep 2, 2012