Definition:Product

Disambiguation

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Product may refer to:

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

• 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: this means either:
    • Group Operation
    • Product Element
  • Ring Product
  • Field Product

• 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

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): product
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): product