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

---

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,mandn, the number of objects in the set formed by combiningmsets, each of which hasnobjects.

For two rational numbers,a/bandc/d, wherea,b,c, anddare integers, the number (ac)/(bd).

For any two real numbers, which are the limits of sequences of rational numbersp_nandq_nrespectively, the limit of the sequencep_nq_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 setsA₁,A₂, …,A_nis the set of all elements of the form (a₁,a₂, …,a_n) where eacha_iis an element ofA_ifor eachi= 1, 2, …,n.

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

For two fuzzy setsAandB, with membership functionsm_Aandm_B, the fuzzy set whose membership functionm_A·Bsatisfies the equationm_A·B(x) =m_A(x) ·m_B(x) for every elementx.

The productABof two matricesAandB, where the numbernof columns inAequals the number of rows inB, is the matrix whose elementc_ijin rowiand columnjis the sum overk= 1, 2, …,nof the product of the elementsa_ikinAandb_kjinB.

---

(mathematics, programming)

product - 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".