# 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.

**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)

(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

*A*_{1},*A*_{2}, …,*A*_{n }is the set of all elements of the form (*a*_{1},*a*_{2}, …,*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".

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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