title: "Surjective"

Surjective

Definition. A Function $f: A \to B$ is surjective if every element of the codomain is hit: for every $b \in B$ there is some $a \in A$ with $f(a) = b$.

Proving surjectivity means producing a preimage for an arbitrary $b$; disproving it means exhibiting one missed $b$ (Quantifier negation). See Injective and Bijection; introduced in Lecture 2, Example 6.