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. 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 | change source]

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 | change source]

( 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 | change source]

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

Related pages[change | change source]

References[change | change source]

  1. "Comprehensive List of Algebra Symbols". Math Vault. 2020-03-25. Retrieved 2020-08-16.
  2. "Summation and Product Notation". math.illinoisstate.edu. Retrieved 2020-08-16.
  3. Weisstein, Eric W. "Product". mathworld.wolfram.com. Retrieved 2020-08-16.