Introduction to Set Theory

In Math, sets are used to define the concept of functions and vector spaces. The original set theory was first introduced by mathematician Georg Cantor.

In math sets is a well-defined collection of objects.

Set Theory Notation and Set Theory Symbols

If ‘a’ is an element of set A then we say that ‘a belongs to A’. The Greek symbol ∈ (epsilon) is used to denote the phrase “belongs to”. Thus we can write  a ∈ A .

If ‘b’ is not an element of A we write b  ∈ B and read “b does not belong to A”.

Set Roster Notation (or tabular form sets):

Examples of set roster notation can be:

E = {2, 4, 6, 8}

The set V of all consonants in the word MISSISSIPPI is described in the roster set notation form as :

While writing the elements in a roaster set form, all elements are taken as distinct and no element is repeated. For example, the set of letters forming the word ‘MISSISSIPPI’ is {M,I,S,P} or {P,M,I,S} or { I, S,M,P} .

Set Builder Notation:

A set builder notation is defined as that form of writing a set in which all elements of a set possess a single common property which is not possessed by an element outside the set.

Null Set definition: A set which does not contain any element is called the null set or the empty set or void set.

Null Set Example: P = { p : 5 < p < 6, p is an integer}

If n(S) is a natural number, then S is a non-empty finite set or definite set.

Example of cardinal number of a set is :

Example of roster set notation of infinite set:

N = { n : n is a natural number } = { 1,2,3,4, … }

W = { w : w is a whole number} = { 0, 1, 2, 3, …}

Equal Sets

Two sets A and B are said to be equal if they have exactly the same elements and we write A = B. Otherwise the sets are said to be unequal and we write A ≠ B.

Example of equal sets can be: Let A = {4,6,8,10,12} and B = { 8,4,10,6,12} . Then A = B