Definition:Product


 * In the context of set theory:
 * The Cartesian product of $S$ and $T$, denoted $S \times T$, is the set of all ordered pairs $\left({s, t}\right)$ where $s \in S$ and $t \in T$.
 * A product $\left({P, \phi_1, \phi_2}\right)$ of $S$ and $T$ is a set $P$ and mappings $\phi_1: P \to S, \phi_2: P \to T$ such that for any set $X$ and any mappings $f_1: X \to S$ and $f_2: X \to T$ there exists a unique mapping $h: X \to P$ such that $\phi_1 \circ h = f_1$ and $\phi_2 \circ h = f_2$.


 * In the context of abstract algebra:
 * Product in the context of a general operation.
 * Group Product in the context of a Group in the field of group theory.
 * Ring Product in the context of a Ring in the field of ring theory.
 * Product in the context of the Naturally Ordered Semigroup.


 * In the context of conventional algebra:
 * In the operation of multiplication of two numbers $a$ and $b$, the product is $a \times b$.


 * In the context of matrix algebra:
 * Matrix Product for various assorted techniques of forming the product of matrices.