Functions: Terminology, Composition, Injectivity & Surjectivity
Function Terminology Formally, a function from $A$ to $B$ is thought of as a relation $f \subseteq A \times B$. Definition 58 (Function Terminology). Let $A$ and $B$ be sets. A relation $f \subseteq A \times B$ is a function from $A$ to $B$ if for each $a \in A$, there is a unique $b \in B$ such that $(a,b) \in f$. When $f$ is a function from $A$ to $B$, we write $f:A \to B$, and: ...