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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.)
     

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  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
     
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