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Math Help - Injective/Surjective

  1. #1
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    Injective/Surjective

    I need to give examples of functions mapping from the natural numbers into the natural numbers with the following properties:

    1. Surjective, not injective

    2. Injective, not surjective
    f(x) = 2x

    3. Neither injective nor surjective

    4. Bijective
    f(x) = x

    I think I figured out (2) and (4) but any help with the other two conditions would be helpful!
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  2. #2
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    Hello,
    Quote Originally Posted by GoldendoodleMom View Post
    I need to give examples of functions mapping from the natural numbers into the natural numbers with the following properties:

    1. Surjective, not injective
    \begin{aligned} f : & \mathbb{N} & \to & \mathbb{N} \\<br />
& n & \mapsto & f(n) \end{aligned}

    \left\{ \begin{array}{lll} f(0)=0 \\<br />
f(1)=0 \\<br />
f(n)=n-1 \quad \forall n \ge 2 \end{array} \right.

    2. Injective, not surjective
    f(x) = 2x


    3. Neither injective nor surjective
    \begin{aligned} g : & \mathbb{N} & \to & \mathbb{N} \\<br />
& n & \mapsto & g(n) \end{aligned}

    \left\{ \begin{array}{lll} g(0)=1 \\<br />
g(1)=1 \\<br />
g(n)=n \quad \forall n \ge 2 \end{array} \right.


    4. Bijective
    f(x) = x
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