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# Product

The term "product" refers to the result of one or more multiplications. 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

 (1)

Useful product identities include

 (2) (3)

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

Portions of this entry contributed by John Renze

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## Cite this as:

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