## HOW TO IDENTIFY THE FOLLOWING SET ARE FINITE OR INFINITE

How to identify the following set are finite or infinite ?

Here we are going to see how to identify the following set are finite or infinite.

## Finite set

If the number of elements in a set is zero or finite, then the set is called a finite set.

## Infinite set

A set is said to be an infinite set if the number of elements in the set is not finite.

## Examples of infinite set

(i)  Consider the set A of natural numbers between 8 and 9.

There is no natural number between 8 and 9.

So, A  =  {  } and n(A) = 0.

Hence, A is a finite set.

(ii)  Consider the set

X  =  { x : x is an integer and -1 ≤ x ≤ 2 }

So, X  =  { -1, 0, 1, 2 } and n(X)  = 4

Hence, X is a finite set.

Note : The cardinal number of a finite set is finite.

## Examples of infinite set

Let W  =  The set of all whole numbers .

That is, W  =  { 0, 1, 2, 3, ......................}

The set of all whole numbers contain infinite number of elements.

Hence, W is an infinite set.

Note : The cardinal number of an infinite set is not a finite number.

Let us look into some more examples for better understanding.

Example 1 :

Identify the following set as finite or infinite

A = {4, 5, 6, ......................}

Solution :

We cannot count the number of elements in the given set.

Hence it is infinite set.

Example 2 :

Identify the following set as finite or infinite

B = {0, 1, 2, 3, 4, ......................,75}

Solution :

The given set has countable number of elements.

Hence it is finite set.

Example 3 :

Identify the following set as finite or infinite

X = {x : x is an even natural number}

Solution :

Since the given set has even natural number, it starts with 2.

X = {2, 4, 6, ...............}

We couldn't find the number of elements in the given set. Hence it is infinite set.

Example 4 :

Identify the following set as finite or infinite

Y = {x : x is a multiple of 6 and x > 0}

Solution :

The elements of the given set set should be multiples of 6.

Y = {6, 12, 18, 24, .....................}

We couldn't find the number of elements in the given set. Hence it is infinite set.

Example 5 :

Identify the following set as finite or infinite

P = The set of letters in the word ‘freedom’

Solution :

The set P contains letters of the word "freedom"

P = { f, r, e, d, o, m }

Set P has countable number of elements. Hence it is finite set.

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