Product (mathematics)

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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. The product of 6 and 4 will be 24, because 6 × 4 = 24.

Capital pi[change | change source]

A short notation for long multiplication expressions is the product notation. It uses the capital Greek letter pi: . This works the same as the Sigma notation. 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[change | change source]

( is pronounced " factorial" or "factorial of ");
, i.e., the usual th power operation;
, i.e., we multiply by itself times;
where is a constant with respect to .

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: one generally cannot separate terms inside them before they are raised to an exponent. But the product does,

Relation to Summation[change | change source]

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