A set is a collection of distinct objects (called elements or members) such that for any object, it can be determined whether the object belongs to the collection. -- Academic Press Dictionary of Science and Technology
The order of elements of a set does not matter. A given element only occurs once in a set. A multiset or bag is similar to a set but allows multiple occurrences of a given element. A set may be finite, such as the set of letters of the alphabet, or infinite, such as the set of integers.
A finite set can be described by enumerating its members. An infinite set can be described by giving a test for membership ( i.e., a predicate).
In mathematical notation, a set is written inside braces: { a, e, i, o, u, y }