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Sets are one of the base concepts of mathematics. A set is, more or less, just a collection of objects, called its elements. Standard notation uses braces around the list of elements, as in:
{red, green, blue} {x : x is a primary color}
As you see, it is possible to describe one and the same set in different ways: either by listing all its elements (best for small finite sets) or by giving a defining property of all its elements.
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, called 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 union and intersection of sets, say A1, A2, A3, ... are denoted A1 u A2 u A3 u ... and A1 n A2 n A3 n ... respectively. If you don't mind jumping ahead a bit, the subsets of a given set form a boolean algebra under these operations. The set of all subsets of X is called its powerset and is denoted 2X or P(X).
Examples of sets of numbers include
Statistical Theory is built on the base of Set Theory and Probability Theory.
For example: Suppose we call a set "well-behaved" if it doesn't contain itself as an element. Now consider the set S of all well-behaved sets. Is S well-behaved? There is no consistent answer; this is Russell's Paradox. In axiomatic set theory, no set can contain itself as an element.