Cardinal Numbers

Cardinal numbers are natural numbers used for counting, typically starting from 1. For example, 8 books, 3 pens, etc. These numbers represent whole quantities and are not expressed as decimals or fractions. Cardinal numbers help in determining the total count of objects, such as children gathered for an activity. The smallest cardinal number is 1 since 0 cannot be used for counting. The number of elements in a set is called its cardinality. For example, the set {2, 4, 6, 8} consists of 4 elements.

Cardinal Numbers Definition

Cardinal numbers are the numbers used to express the total amount of items in a group. They indicate the exact count of objects starting from 1 and increasing in order. 


Cardinal Numbers Examples:

Some of the examples of cardinal numbers are: 
 

• If a basket has apples, we count them using cardinal numbers like one apple, two apples, three apples, and so on. 
   
• When the total number of students in a classroom is asked, the count is given as cardinal numbers, such as 30 or 40. 
   
• A student says he has three pencils, two pens, and one eraser in his bag. He is using cardinal numbers. 

The numbers in the examples above are examples of cardinal numbers. It denotes a quantity of something, where the order is not essential. And these counts are not given as decimals or fractions; they are only provided as counting numbers. 

Cardinal Numbers in English
 

Cardinal numbers are the basic numbers we use to count things and to say how many items are present. For example, 4 men are working on the site, or I have 5 books with me. 
These numbers can be written in words in English, and the cardinal numbers in English for the first 10 numbers are given below: 
 

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

The list of cardinal numbers from 1 to 100 forms the basis for understanding more complex numbers. Now, let’s look at a table that displays the counting numbers from 1 to 100:

Cardinal numbers 100 to 1000
 

Now, let us look at the list of cardinal numbers from 100 to 100, which are the multiples of 100. 

Large Cardinal Numbers
 

Large cardinal numbers will be useful when a large quantity of objects has to be represented. For example, 10,000 people are attending the event. Now let us see a few large cardinal numbers. 

There are two types of numerical representations: cardinal and ordinal numbers. To learn how they differ from one another, we will now look at their key differences:

The cardinal number of a set refers to the total number of distinct elements present in that set. It tells us how many items the set contains, regardless of what those items are. For a finite set, this is a natural number (1, 2, 3,…). For example, if A = {2, 4, 6, 8, 10}, then |A| = 5. For an empty set E = {}, we have |E| = 0. 

 

What is Cardinality?

The term cardinality refers to the size of a set, that is, the total number of elements contained in the set. For a set A, the cardinality is often written as |A| or n(A). Cardinality applies to both finite sets and infinite sets. If the set has a limited number of elements, its cardinality is some natural number. If the set is infinite, then its cardinality may be infinite. 
For example, let A = {a, b, c, d}. Then the cardinality of A is 4, because there are four distinct elements. We can write it as: |A| = 4. 
 

Here are some of the tips and tricks for a better understanding and effective usage of cardinal numbers. 

• You can identify a cardinal number by identifying "how many?" in a question. The answer to such questions are usually a cardinal number.
   
• Always keep in mind that zero is also a cardinal number, meaning no quantity.
   
• Watch out for singular and plural forms. Use singular for 1 and use plural for 2 or more.
   
• Remember place values, as each digit's value depends on its place.
   
• Always remember that cardinal numbers show quantity, unlike ordinal numbers that show the order.
   
• Parents and teachers can encourage students to count everyday objects like toys or fruits, to become thorough with cardinal numbers.
   
• Parents and teachers can also use simple questions, such as “how many do you see?”, to help students learn naturally.
   
• Provide opportunities for hands-on counting, such as sorting items or grouping objects, so students can use cardinal numbers.
   
• Help students differentiate between counting numbers, which are cardinals, and position words, which are ordinals, through examples.
   
• Give clear examples, using real-life scenarios, to help students understand the concept of zero. For example, telling them that there are zero cookies left. 
   

Cardinal numbers are used in real-life situations to count or measure quantities. We will now look at a few examples to learn how they can be applied:

• Cardinal numbers are fundamental in everyday situations like counting the number of family members, furniture, or other objects.

• These numbers aid in time management by tracking the hours spent on screens, sleeping, and other activities. 

• Cardinal numbers help children count money or make financial decisions, such as calculating the amount to be saved.

• Sports coaches can count the number of players or maintain the score of each player.