A numerical product is the result of the multiplication of its factors. A product of a single factor is that factor itself, and an empty product is defined to be 1. For example, the mathematical statement would be read " times equals ," where is called the multiplier, the multiplicand and is their product. In addition, and are factors of .

More generally, it is possible to take the product of many different kinds of mathematical objects, including those that are not numbers. For example, the product of two sets is given by the Cartesian product. In topology, the product of spaces can be defined by using the product topology. The product of two groups, vector spaces, or modules is given by the direct product. In category theory, the product of objects is given using the category product.

The product symbol is defined by

For positive factors such that the series converges, useful product identities include

See also

Cartesian Product, Category Product, Cauchy Product, Cross Product, Cumulative Product, Direct Product, Dot Product, Empty Product, Factor, Graph Product, Inner Product, Jordan Product, Matrix Product, Multiplicand, Multiplication, Multiplier, Nonassociative Product, Prime Products, Product Topology, Sum, Times, Vector Triple Product

Portions of this entry contributed by John Renze

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Cite this as:

Weisstein, Eric W., with contributions by John Renze. "Product." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Product.html

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