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 times 4 is 24.
Use of (one form) of thhgreek letter "Π" (or "pi")Edit
A short way to write the product of many numbers uses the capital Greek letter pi: . This notation (or way of writing) is in some ways similar to 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 .
- ( is pronounced " factorial" or "factorial of ");
- , i.e., the usual th power operation;
- , i.e., we multiply 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: one generally cannot separate terms inside them before they are raised to an exponent. But the product does,
Relation to SummationEdit
The product of powers with the same base can be written as an exponential of the sum of the powers' exponents: