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Definition

# product

1) In information technology, a product is something (for example, a software application) that is created and then made available to customers, usually with a distinct name or order number.

2) In mathematics, a product is the result of arithmetically multiplying numbers or quantities. There can be as few as two terms, or as many as a hundred, a thousand, or a million. Some products contain infinitely many terms.

For products with relatively few terms, the numbers, or multiplicands, can be written one after another, separated by multiplication signs (x). An example is 1/1 x 1/2 x 1/3. This becomes awkward when the number of terms is large. When a product has infinitely many terms, the terms must occur in a definable sequence. This sequence is not always clear when the terms are simply listed and separated by multiplication symbols. For this reason, the product symbol was devised: a large, uppercase Greek letter pi.

To denote 1/1 x 1/2 x 1/3, the following symbology can be used:

The expression on the left-hand side of the equation is the product from n = 1 to n = 3 for 1/ n . The value of n is always an integer. It usually starts at 1 and always increases by 1 for each succeeding term in the product.

Suppose the above sequence of multiplicands is extended without limit according to the obvious pattern. Then the product from n = 1 to unlimited values of n for 1/ n , that is, 1/1 x 1/2 x 1/3 x 1/4 x ..., is denoted like this:

The sideways 8 (called a lemniscate ) means that n continues to increase without limit. It is imprecise to say we are dealing with the product from n = 1 to infinity , but this terminology is often used anyway.

Also see Mathematical Symbols .

This was last updated in September 2005
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