Home » sets » SETS : DEFINITION

The word ‘set’ in mathematics was first used by a German mathematician George Cantor (1845 – 1918).

A set is a well-defined collection of objects. Well – defined means universal truth. The elements do not varies person to person.

Set is denoted by capital letters of English alphabets. E.g. A, B, C, D, F, G, K, Y, Z etc. It is written in { } bracket always.


1. The collection of all states in India is a set. But the collection of all god states in India is not a set. [Good states is not well – defined, it varies person to person].

2. The collection of all teachers in a school is a set. But the collection of all good teachers is not a set.

Some examples of sets are given below:

1. The collection of vowels in English alphabet.

2. The collection of first five natural numbers.

3. The collection of all girls in class X in a school.

4. The collection of months having 31 days.

5. The collection of all chief ministers in India.

Some examples of not a set are given below:

1. The collection of good students in your class.

2. The collection of difficult topic in mathematics.

3. The collection of beautiful girls in your class.

4. The collection of good cricket players in the world.

Elements in a set is written as a ∊ A, “∊ is read as belongs to”, and means “a” is an element of set A.

For example: A = {a, e, i, o, u}

a ∊ A

e ∊ A

i ∊ A

o ∊ A

u ∊ A

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