product

product

1. a substance formed in a chemical reaction

2. Maths the result of the multiplication of two or more numbers, quantities, etc.

3. See Cartesian product

Collins Discovery Encyclopedia, 1st edition © HarperCollins Publishers 2005

product

[′präd·əkt]

(chemistry)

A substance formed as a result of a chemical reaction.

(chemical engineering)

discharge liquor

(industrial engineering)

An item or goods made by an industrial firm.

The total of such items or goods.

(mathematics)

For two integers, m and n, the number of objects in the set formed by combining m sets, each of which has n objects.

For two rational numbers, a/b and c / d, where a, b, c, and d are integers, the number (ac)/(bd).

For any two real numbers, which are the limits of sequences of rational numbers p_n and q_n respectively, the limit of the sequence p_n q_n .

The product of two algebraic quantities is the result of their multiplication relative to an operation analogous to multiplication of real numbers.

The product of a collection of sets A₁, A₂, …, A_n is the set of all elements of the form (a₁, a₂, …, a_n ) where each a_i is an element of A_i for each i = 1, 2, …, n.

For two transformations, the transformation that results from their successive application.

For two fuzzy sets A and B, with membership functions m_A and m_B , the fuzzy set whose membership function m_A·B satisfies the equation m_A·B (x) = m_A (x) · m_B (x) for every element x.

The product AB of two matrices A and B, where the number n of columns in A equals the number of rows in B, is the matrix whose element c_ij in row i and column j is the sum over k = 1, 2, …, n of the product of the elements a_ik in A and b_kj in B.

McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.

product

(mathematics, programming)

An expression in mathematics or computer programming consisting of two other expressions multiplied together. In mathematics, multiplication is usually represented by juxtaposition, e.g. "x y", whereas in programming, "*" is used as an infix operator, e.g. "salary * tax_rate.

In the most common type of product, each operand is a number (integer, real number, fraction or imaginary number) but the term extends naturally to cover more complex operations like multiplying a string by an integer (e.g., in Perl, "foo" x 2) or multiplying vectors and matrices or more than two operands.

In type systems, a tuple is sometimes known as a "product type".

This article is provided by FOLDOC - Free Online Dictionary of Computing (foldoc.org)