Definition:Product


 * Arithmetic and conventional algebra
 * In the operation of multiplication of two numbers $a$ and $b$, the product is $a \times b$.
 * Product Notation: $\displaystyle \prod_{j \mathop = 1}^n a_j = \paren {a_1 \times a_2 \times \cdots \times a_n}$


 * Set Theory:
 * The Cartesian product of $S$ and $T$, denoted $S \times T$, is the set of all ordered pairs $\tuple {s, t}$ where $s \in S$ and $t \in T$.
 * A product $\struct {P, \phi_1, \phi_2}$ 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 $\phi_2 \circ h = f_2$.
 * The product of cardinals.


 * 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.


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


 * Definition:Intersection Product
 * Definition:Product (Category Theory)

Also see

 * Definition:Factor
 * Definition:Quotient
 * Definition:Sum