**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 setIf the number of elements in a set is zero or finite, then the set is called a finite set. |
## Infinite setA set is said to be an infinite set if the number of elements in the set is not finite. |

(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.

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.

After having gone through the stuff given above, we hope that the students would have understood "How to identify the following set are finite or infinite".

Apart from the stuff given above, if you want to know more about "How to identify the following set are finite or infinite", please click here

Apart from the stuff, "How to identify the following set are finite or infinite", if you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...

**WORD PROBLEMS**

**HCF and LCM word problems**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**