Product (mathematics)

result of multiplying

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.also if you times 2 negative numbers it will be positive

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  .

PropertiesEdit

  (  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: