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Product
The word product in mathematics generally means the result of some type of multiplication operation, i.e.
of certain types of mapping
; such operations are commonly distributive
over the addition operation of 
if it is defined.
If 
and 
are two elements of the set 
, giving the product 
, then 
and 
are in general called the factors of this product.
Some most usual products are
- the ring product (also in fields), especially the product of numbers and the product of square matrices;
- on vectors the scalar product, the vector product, the dyad product and the Hadamard product; on ideals the product of ideals;
- the Cartesian product, the direct products
of various systems (not in connection with any additions).
Such kinds of product that are associative, allow to form a product of more than two factors, which is justified by the theorem in the entry general associativity. E.g. the usual product of the integers
from 1 to 
is the factorial
of 
.