Cardinal Numbers

The cardinal numbers are the numbers that are used for counting something. These are also said to be cardinals. These are the natural numbers that start from 1 and goes on sequentially and are not fractions. 

The examples of cardinal numbers are: 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,….

The meaning of cardinals is ‘how many’ of anything is existing in a group. Like if we want to count the number of apples present in the basket, you have to make use of these numbers, such as 1, 2, 3, 4, 5….and so on. The numbers help us to count the number of things or people present in a place or a group. The cardinal numbers denote the collection of all the ordinal numbers.

Definition

As we already discussed, the numbers which can be counted are the cardinals. It means all the natural numbers come in this category. Therefore, we can write the list of cardinal numbers as;

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, ……, 50, 51, 52, 53, 54, …., 99, 100, 101, 102, 103, 104, 105, ……, 999, 1000,…..,∞

So, with the help of these numbers given in the table above, we can define the counting of the objects or persons or animals or other things.

Cardinal Examples

The cardinality of a group represents the number of objects available in that group.

  1. There are 6 clothes in the cupboard.
  2. 4 cars are driving in a lane.
  3. Anusha has 2 dogs and 1 cat as pets in her house.

In the above three examples, the numbers 6, 4, 2 and 1 are the cardinal numbers. So basically it denotes the quantity of something, irrespective of their order. It defines the measure of the size of a set but does not take account of the order.

The set of finite numbers are the natural numbers that define cardinality. Whereas, the set of infinite cardinals describes the size of infinite sets. The cardinals don’t have any fractions or decimals; they have only counting numbers.

Cardinal Numbers of a Set

The number of elements or members in a set is the cardinal number of that set. If A is a finite set and it has elements equal to N. Then the cardinal number of set A is N. 

Note: The cardinal number of an empty set is always zero.

For example, set A = {1, 3, 6, 9, 10, 12, 18}, the cardinal number of set A is 7. Hence, n(A) = 7

Thus, the only formula for counting numbers is to find the number of elements of any set.

Cardinal Numbers in English

Cardinal numbers define how many things or people are there. For example:

  • Five men are standing on a ship.
  • There eight fruits kept in a basket.

These numbers are written in English in the same way, and we write numbers in words. For the first 10 numbers, we can write here:

  • 1-One
  • 2-Two
  • 3-Three
  • 4-Four
  • 5-Five
  • 6-Six
  • 7-Seven
  • 8-Eight
  • 9-Nine
  • 10-Ten

Ordinal Numbers

The ordinal numbers are the numbers which denote the position of something. If several objects are mentioned in a list, the order of the objects is defined by ordinal numbers. The adjective terms which are used to denote the order of something are 1st, 2nd, 3rd, 4th, 5th, 6th, and so on.

Examples:

  1. Anil came to 3rd position in a running competition.
  2. The 6th chair is broken in a hall.

Cardinal and Ordinal Numbers Chart (1-100)

Let us create a chart table where we will write the cardinal numbers and equivalent ordinal numbers.

Cardinals Ordinals Cardinals Ordinals
1, One 1st, First 11, Eleven 11th, Eleventh
2, Two 2nd, Second 12, Twelve 12th, Twelfth
3, Three 3rd, Third 13, Thirteen 13th, Thirteenth
4, Four 4th, Fourth 14, Fourteen 14th, Fourteenth
5, Five 5th, Fifth 15, Fifteen 15th, Fifteenth
6, Six 6th, Sixth 16, Sixteen 16th, Sixteenth
7, Seven 7th, Seventh 17, Seventeen 17th, Seventeenth
8, Eight 8th, Eighth 18, Eighteen 18th, Eighteenth
9, Nine 9th, Ninth 19, Nineteen 19th, Nineteenth
10, Ten 10th, Tenth 20, Twenty 20th, Twentieth

After 20, the denotation or pattern of Ordinal numbers changes as;

21, Twenty-One 21st, Twenty-First 26, Twenty Six 26th, Twenty-Sixth
22, Twenty-two 22nd, Twenty-second 27, Twenty Seven 27th, Twenty-Seventh
23, Twenty-three 23rd, Twenty-third 28, Twenty Eight 28th, Twenty-Eighth
24, Twenty-four 24th, Twenty-fourth 29, Twenty Nine 29th, Twenty-Ninth
25, Twenty-five 25th, Twenty-fifth 30, Thirty 30th, Thirtieth

In the same way, we can write the numbers till infinity following the same order, after 30 or 30th.

To practice, students can write the ordinals after numbers such as 40, 50, 60, 70, 90, 100, as per given below;

Cardinals Ordinals
40, Forty 40th, Fortieth
50, Fifty 50th, Fiftieth
60, Sixty 60th, Sixtieth
70, Seventy 70th, Seventieth
80, Eighty 80th, Eightieth
90, Ninety 90th, Ninetieth
100, Hundred 100th, Hundredth

Cardinal Numbers 100 to 1000

100 One hundred
200 Two hundred
300 Three hundred
400 Four hundred
500 Five hundred
600  Six hundred
700 Seven hundred
800  Eight hundred
900 Nine hundred
1000 One thousand

More:

10,000 Ten Thousand
100,000 One hundred thousand
1,000,000 One million
10,000,000 Ten million

Nominal Numbers

The nominal numbers are used to name an object or a thing in a set of group. It is used for the identification of something. It is not for representing the quantity or the position of an object.

Examples:

  1. Model numbers of Vehicles.
  2. Pincodes of various cities.

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Frequently Asked Questions – FAQs

What is a cardinal number? Give example.

A cardinal number represents “how many” or “number of” elements in a set or group.
Example: there are 5 flowers in a vase, then 5 shows the cardinality of flowers.

How is cardinal number different from ordinal number?

Cardinal number represents the count of anything whereas ordinal number refers to the position of an object or a person.

What is nominal number?

Nominal numbers denotes the name of an object or person. The number plate of vehicle is an example of nominals.

What is the cardinal number of set A = {3,5,7,9,10,11,4,19}?

Set A contains 8 number of elements. Therefore, cardinal number for set A is 8.

Which is the smallest cardinal number?

The smallest cardinal number is 1.

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