Product (mathematics)

In mathematics, a product is a number or a quantity obtained by multiplying two or more numbers together. For example:  4 × 7 = 28  Here, the number 28 is called the product of 4 and 7. As another example, the product of 6 and 4 is 24, because 6 times 4 is 24. The product of two positive numbers is positive, just as the product of two negative numbers is positive as well (e.g., -6 × -4 = 24).

 Pi product notation 
A short way to write the product of many numbers is to use the capital Greek letter pi: . This notation (or way of writing) is in some ways similar to the Sigma notation of summation.

Informally, given a sequence of numbers (or elements of a multiplicative structure with unit) say  we define . A rigorous definition is usually given recursively as follows

An alternative notation for  is .
 Properties 
 ( is pronounced " factorial" or "factorial of ")
 (i.e., the usual th power operation)
 (i.e.,  multiplied by itself  times)
 (where  is a constant independent of )
From the above equation, we can see that any number with an exponent can be represented by a product, though it normally is not desirable.

Unlike summation, the sums of two terms cannot be separated into different sums. That is,
, 
This can be thought of in terms of polynomials, as one generally cannot separate terms inside them before they are raised to an exponent, but with products, this is possible:

 Relation to Summation 
The product of powers with the same base can be written as an exponential of the sum of the powers' exponents:

 Related pages 

 Cartesian product
 Cross product
 Dot product

 References 

Category:Arithmetics