The notation "f: X → Z" represents a function named "f" that maps elements from set X to set Z. In this context, X is the domain, which contains all possible input values, while Z is the codomain, which includes all potential output values. Each element in X is associated with exactly one element in Z. Functions like "f" are fundamental in mathematics, as they describe relationships between different sets. For example, if X consists of numbers and Z consists of their squares, then the function "f" takes each number from X and produces its square in Z.