title: "Injective"

Injective

Definition. A Function $f: A \to B$ is injective if distinct inputs give distinct outputs: $f(a) = f(a')$ implies $a = a'$.

Proving injectivity is a "for all" argument (assume $f(a) = f(a')$, derive $a = a'$); disproving it needs one collision pair as a witness (Quantifier shapes). See Surjective and Bijection; introduced in Lecture 2, Example 6.