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set (sh)




In mathematics and logic, any collection of objects (elements), which may be mathematical (e.g., numbers, functions) or not.

The intuitive idea of a set is probably even older than that of number. Members of a herd of animals, for example, could be matched with stones in a sack without members of either set actually being counted. The notion extends into the infinite. For example, the set of integers from 1 to 100 is finite, whereas the set of all integers is infinite. A set is commonly represented as a list of all its members enclosed in braces. A set with no members is called an empty, or null, set, and is denoted ?. Because an infinite set cannot be listed, it is usually represented by a formula that generates its elements when applied to the elements of the set of counting numbers. Thus, {2x|x = 1,2,3,...} represents the set of positive even numbers (the vertical bar means "such that").