ABSTRACT
A set is a collection of objects of a certain kind, which are called elements of the set. We typically denote a set by a capital Greek or Latin letter, i.e., A,B,Σ, . . ., and an element of a set by a small letter, such as a, b, c, . . .. A set may be given by the list of its elements, for example, A = {a, b, c} or B = {1, 2}, or by some clearly defined rules, which can be used to determine whether a given object is an element of the given set. For example, the set of all real numbers between 0 and 1, inclusive, can be equivalently represented in several different ways as follows:
X = {x : x2 − x ≤ 0} = {x : 0 ≤ x ≤ 1} = {x : x ∈ [0, 1]} = [0, 1].
