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.
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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.
- There are 6 clothes in the cupboard.
- 4 cars are driving in a lane.
- 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:
- Anil came to 3rd position in a running competition.
- 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:
- Model numbers of Vehicles (Eg, MH-03-1000)
- 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
- Ordinal Numbers
- Numbers
- Introduction to Large Numbers
- Missing Numbers
- Natural Numbers and Whole Numbers
- Numbers In Words
Frequently Asked Questions – FAQs
What is a cardinal number? Give example.
Example: there are 5 flowers in a vase, then 5 shows the cardinality of flowers.