1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Injective functions

  1. Nov 2, 2009 #1
    1. The problem statement, all variables and given/known data
    Mark as true or false.
    (a) A function is injective if a 6[tex]\neq[/tex] b yields f(a) 6[tex]\neq[/tex] f(b).
    (b) A function is injective if f(a) = f(b) in case that a = b.
    (c) A function is injective if f(a) = f(b) only if a = b.
    (d) A function is injective only when f(a) 6[tex]\neq[/tex] f(b) yields a 6[tex]\neq[/tex] b.





    3. The attempt at a solution

    a) False
    b) True
    c) True
    d) True





    I know that f is said to be injective, if and only if f(a) = f(b) implies that a = b.




    1. The problem statement, all variables and given/known data

    Mark as true or false. If f : E ! E is a map on a finite set then
    (a) If f is injective then f is surjective.
    (b) If f is surjective then f is injective.
    (c) There is an injective map f from the set of natural numbers N to itself which is not surjective.
    (d) There is a surjective map f from the set of natural numbers N to itself which is not injective.

    I don't really get this. Probably easy, but badly explained in the book. Can someone clarifiy this one for me, please?

    Thank you
     
    Last edited: Nov 2, 2009
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted



Similar Discussions: Injective functions
Loading...