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
 |
(1)
|
For positive factors 
such that the series 
converges,
useful product identities include
 |  |  |
(2)
|
 |  |  |
(3)
|
