## setA finite or infinite collection of objects known as elements.
Sets are one of the most basic and important concepts in mathematics. An
example of finite set is the set of whole numbers from 1 to 58; an example
of an infinite set is the set of all the rational
numbers. Two sets are equal if, and only if, they contain the same objects. Standard set notation uses braces around the list of elements, as in: {red, green, blue}. If A and B are two sets and every x in A is also contained in B, then A is said to be a subset of B. If A and B are two sets and every x in A is also contained in B, then A is said to be a
subset of B. Every set has as subsets itself, known as the improper
subset, and the empty set. The union of a collection of sets S = {S_{1}, S_{2}, S_{3}, ...} is the set of all elements
contained in at least one of the sets S_{1}, S_{2}, S_{3}, ... The intersection of a collection
of sets T = {T_{1}, T_{2}, T_{3},
...} is the set of all elements contained in all of the sets. The set of
all subsets of X is called its power set and is
denoted 2^{X} or P(X). A universal set is a set containing all the elements with a certain property. It is also the name given to a hypothetical set which could include everything. Such an all-encompassing set contradicts the basic notion of a set. The mathematical theory of sets (see set theory) was firstinvestigatedby Georg cantor (1845–1918) and later systematized by Ernst Zermelo (1871–1956)., but the basic concepts were known earlier. ## Related entries## Related category• SETS AND SET THEORY | |||||

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