# Set, definition, types, notation, and examples

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?

• A={…,-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7}

• B={2, 4, 6, 8, 10, 12,14,16,18, 20…256}

• C={-4, -3, -2, -1, 0, 1, 2, 3, 4,…}

Practice 2: which of the following is a unit set

• A={All capital cities in the United States of America}

• B={Months in a year with names beginning with the letter A}

• C={ Soft drinks in the US }

For ways of describing a set click here