Different Notations in Sets

What are the different notations in sets?

To learn about sets we shall use some accepted notations for the familiar sets of numbers.

Some of the different notations used in sets are:

: or |




I or Z







Belongs to 

Does not belongs to 

Such that

Null set or empty set

Cardinal number of the set A

Union of two sets

Intersection of two sets

Set of natural numbers = {1, 2, 3, ……}

Set of whole numbers = {0, 1, 2, 3, ………}

Set of integers = {………, -2, -1, 0, 1, 2, ………}

Set of all positive integers

Set of all rational numbers

Set of all positive rational numbers

Set of all real numbers

Set of all positive real numbers

Set of all complex numbers

These are the different notations in sets generally required while solving various types of problems on sets.


(i) The pair of curly braces {  } denotes a set. The elements of set are written inside a pair of curly braces separated by commas.

(ii) The set is always represented by a capital letter such as; A, B, C, …….. .

(iii) If the elements of the sets are alphabets then these elements are written in small letters.

(iv) The elements of a set may be written in any order.

(v) The elements of a set must not be repeated.

(vi) The Greek letter Epsilon ‘∈’ is used for the words ‘belongs to’, ‘is an element of’, etc.

Therefore, x ∈ A will be read as ‘x belongs to set A’ or ‘x is an element of the set A'.

(vii) The symbol ‘∉’ stands for ‘does not belongs to’ also for ‘is not an element of’.

Therefore, x ∉ A will read as ‘x does not belongs to set A’ or ‘x is not an element of the set A'.

Set Theory


Objects Form a Set

Elements of a Set

Properties of Sets

Representation of a Set

Different Notations in Sets

Standard Sets of Numbers

Types of Sets

Pairs of Sets


Subsets of a Given Set

Operations on Sets

Union of Sets

Intersection of Sets

Difference of two Sets

Complement of a Set

Cardinal number of a set

Cardinal Properties of Sets

Venn Diagrams

7th Grade Math Problems

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