Cardinal Numbers

The cardinal numbers are the numbers that are used for counting something. These are also said to be cardinals. The cardinal numbers are the counting 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.

What are Cardinal Numbers?

As we already discussed, the numbers that are used for counting are called cardinal numbers. 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, we can form different cardinal numbers based on the counting of objects.

Cardinal Numbers 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 in English

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

  • Five men are standing on a ship.
  • There are 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

List of Cardinal Numbers

Here is the list of cardinal numbers from 1 to 20 written in English.

1 – One 6 – Six 11 – Eleven 16 – Sixteen
2 – Two 7 – Seven 12 – Twelve 17 – Seventeen
3 – Three 8 – Eight 13 – Thirteen 18 – Eighteen
4 – Four 9 – Nine 14 – Fourteen 19 – Nineteen
5 – Five 10 – Ten 15 – Fifteen 20 – Twenty

Cardinal Numbers in Multiples of 10

Another set of cardinal numbers is given below, representing the multiples of 10.

10 – Ten 60 – Sixty
20 – Twenty 70 – Seventy
30 – Thirty 80 – Eighty
40 – Forty 90 – Ninety
50 – Fifty 100 – Hundred

The above cardinal numbers are commonly used for counting.

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

Larger Cardinal Numbers

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

The large cardinal numbers are used when a bulk of objects or people or amount has to be represented. For example, the population of a city is 100,000 (one lakh).

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.

What is Cardinality?

The cardinality of a group or a set represents how many objects or elements are actually present in a group or in a set.

For example, if a pen-set has 7 pens in it, then the cardinality of pens is 7.

Difference Between Cardinal number and Ordinal Numbers

The ordinal numbers are different from cardinal numbers. Ordinals are the numbers that 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 Numbers Ordinal Numbers
They are used for counting purpose They are used to denote rank or position or order of something or someone
Examples: 1, 2, 3, 5, 6, 10, etc. Examples: 1st, 2nd, 5th, 6th, 9th, etc
Question type: ‘How many?’

For example: How many balls are there?

Question: ‘Where’ or ‘Which’

For example: Where is this located in the field? Or Which position does it hold in the ground?

Nominal Numbers

The nominal numbers are another type of numbers, different from cardinals and ordinals, used to name an object or a thing in a set of groups. 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 (Eg, MH-03-1000)
  2. Pincodes of various cities. (Eg. 481020)

Facts

  • Cardinal numbers are also called counting numbers and natural numbers
  • All the cardinal numbers can be written in words
  • A group of ordinal numbers can be represented by cardinal numbers
  • Cardinal numbers are always used to count and are stated by ‘how many’
  • Fractions and decimals are not cardinal numbers
  • Zero (0) is not a cardinal number, since it means nothing
  • Cardinality of a set represents how many objects or elements are there in the set

Related Articles To Cardinal Numbers


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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