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Math Help - injection

  1. #1
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    injection

    f:\emptyset\to Y
    is function f injective? as we know, it is, if:
    x,y \in \emptyset
    f(x)=f(y)\Rightarrow x=y
    so left side is always false, because x and y cant be elements of empty set? and then f is always injective?
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  2. #2
    Super Member
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    Yes, f is always injective. To make it clearer, consider this:

    f is not injective iff \exists x, y \in \emptyset  \ s.t. \ x \neq y, f(x) = f(y). Obviously, this can't happen.
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