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!

Homework Help: Exhibit a bijection between N and the set of all odd integers greater than 13

  1. Aug 29, 2010 #1
    1. The problem statement, all variables and given/known data

    Exhibit a bijection between N and the set of all odd integers greater than 13

    2. Relevant equations

    3. The attempt at a solution
    I didn't have a template for the problem solving. Please check if I did it in the right way? (The way and order a professor will like to see.)

    Attached Files:

    • pic.jpg
      File size:
      19 KB
  2. jcsd
  3. Aug 29, 2010 #2
    Almost...your injection proof is fine. But, when proving a mapping is surjective, we need to show that the domain maps all of the range, i.e., show that for each y, there's an x such that f(x) = y.

    You wrote "for y E N," but that's not true. y E B = set of all odd integers greater than 13, not all natural numbers.

    So, basically, what you have to do in the surjective proof here is show that if y is an odd integers greater than 13, then x must be a natural number and thus exist in our domain.
  4. Aug 29, 2010 #3
    Should I do this in math induction?
  5. Aug 29, 2010 #4
    hmm, im not sure if i'm right. but when you define a function [tex]f(x)=2x+13[/tex] don't say [tex]for \ all \ x \in N [/tex] yet, because that is what you suppose to show.

    so just define this function [tex]f(x)=2x+13[/tex]

    like Raskolnikov suggested. any y in the codomain has the form of 2q+13, where q are natural number

    so, like you did, we solve for [tex]y=2x+13 \Rightarrow 2q+13=2x+13[/tex], so you want to show that x is natural number ie: x is the set of the domain
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook