In day-to-day life, we generally talk about a group or a collection of objects. e.g. a pack of cards, a group of students, a group of friends, etc.
- The well-defined collection of objects is called a set.
- Capital English letters A, B, C, etc. are used to denote a set.
- The individual object of the set is known as the member or an element of the set.
- The elements of the set are denoted by lower case letters a, b, c, etc.
- If a is an element of set A, then it is written as a ∈ A, and is read as 'a is an element of set A' or 'a is a member of set A' or 'a belongs to set A'.
- If a is not an element of set A, then it is written as a ∉ A. The symbol ∉ stands for 'is not an element of' or 'is not a member of'. Thus, it is read as 'a is not an element of set A' or 'a is not a member of set A' or 'a does not belong to set A'.
Let us see the set of numbers:
- (a) A set of natural numbers. N = {1, 2, 3, ...}
- (b) A set of whole numbers. W = {0, 1, 2, .....}
- (c) A set of integers. I = {... -3, -2, -1, 0, 1, 2, 3, ....}
- (d) Q is the set of rational numbers.
- (e) R is a set of real numbers.