how to show a function is not injective
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To show a function is not injective we must show ¬[(∀x ∈ A)(∀y ∈ A)[(x = y) → (f(x) = f(y))]]. This is equivalent to (∃x ∈ A)(∃y ∈ A)[(x = y) ∧ (f(x) = f(y))]. Thus when we show a function is not injective it is enough to find an example of two different elements in the domain that have the same image. not surjective.
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