# product

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## product

1. a substance formed in a chemical reaction
2. Maths the result of the multiplication of two or more numbers, quantities, etc.

## product

[′präd·əkt]
(chemistry)
A substance formed as a result of a chemical reaction.
(chemical engineering)
(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 pn and qn respectively, the limit of the sequence pn qn .
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, …, An is the set of all elements of the form (a1, a2, …, an ) where each ai is an element of Ai 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 mA and mB , the fuzzy set whose membership function mA·B satisfies the equation mA·B (x) = mA (x) · mB (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 cij in row i and column j is the sum over k = 1, 2, …, n of the product of the elements aik in A and bkj in B.

## 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".
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