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