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A 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 = {S1, S2, S3, ...} is the set of all elements contained in at least one of the sets S1, S2, S3, ... The intersection of a collection of sets T = {T1, T2, T3, ...} 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 2X 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.


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   • SETS AND SET THEORY