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. 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 change

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.[1]

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  .[2][3]

Properties change

  (  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 change

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


Related pages change

References change

  1. "Comprehensive List of Algebra Symbols". Math Vault. 2020-03-25. Retrieved 2020-08-16.
  2. "Summation and Product Notation". Archived from the original on 2023-08-29. Retrieved 2020-08-16.
  3. Weisstein, Eric W. "Product". Retrieved 2020-08-16.