A set is a collection of well-defined objects of the same kind. Or a set is a collection of distinct objects of the same kind. For example, a collection of flowers, a set of even numbers, etc.
A set is denoted or represented by a capital letter. For instance A, B, P, Q, etc. A set contains objects or elements. All the elements in a set are enclosed by curly bracket { }. So we can say set A={1, 3, 5, 7}. The numbers 1, 3, 5, and 7 are the members or elements of the set.
Types of a set
1. Infinite set: a set whose last member cannot be found or is unknown. For instance set of all integers is an infinite set. The set A={1, 2, 3, 4, 5, 6, 7, 8,…}. Note that the three dots at the end means that the members of set A continue indefinitely. All the members or objects of an infinite set cannot be counted.
2. Finite set: a set whose last member can be found or known. For example, the set Q={ 2, 3, 5, 7, 11} is a finite set with five members. Note that for the finite set, the objects or components of the set can be counted.
3. Unit set: a type of set with only one member or object or component is called a unit set. For instance, the set B={ 7 } is a unit set with only one member. Also, the set A={ 0 } is a unit set with only one member which is zero.
4. Empty set or Null set: is a type of set which has no member or element. Mostly, a null or empty set is represented or denoted by { } or ∅.
5. Universal set: a set of all the elements or objects under discussion. For instance, if the set of Elective mathematics students is taken under discussion in a class, then the set of all students in the class will be the universal set. A universal set is often denoted or represented by ξ or ∪. A universal set is often represented by a rectangle in a Venn diagram.
Practice on set
Try this: which of the following is finite and which of them is infinite?
