What is a cardinal number word

Cardinal versus ordinal numbers

Cardinal one two three four
1 2 3 4
Ordinal first second third fourth
1st 2nd 3rd 4th

A cardinal numeral (or ‘cardinal number word’) is a part of speech used to count.

Examples are the words one, two, three, and also compounds like three hundred and forty-two (Commonwealth English) or three hundred forty-two (American English).

Cardinal numbers are definite numerals. They are related to ordinal numbers, such as first, second, third, etc.[1][2][3]

Related pages[change | change source]

  • Arity
  • Cardinal number for the related usage in mathematics

References[change | change source]

  1. ↑ David Crystal (2011). Dictionary of Linguistics and Phonetics (6th ed.). John Wiley & Sons. p. 65. ISBN 978-1-405-15296-9.
  2. ↑ Hadumo Bussmann (1999). Routledge Dictionary of Language and Linguistics. Taylor & Francis. ISBN 978-0-415-20319-7.
  3. ↑ James R. Hurford (1994). Grammar: A Student’s Guide. Camsixbridge University Press. pp. 23–24. ISBN 978-0-521-45627-2.

This short article about mathematics can be made longer. You can help Wikipedia by adding to it.

Источник

From Wikipedia, the free encyclopedia

This article is about the linguistic concept. For numbers used to measure the size of sets, see Cardinal number.

Cardinal versus ordinal numbers

Cardinal Ordinal
one 1 first 1st
two 2 second 2nd
three 3 third 3rd
four 4 fourth 4th
five 5 fifth 5th
six 6 sixth 6th
seven 7 seventh 7th
eight 8 eighth 8th
nine 9 ninth 9th
ten 10 tenth 10th

In linguistics, and more precisely in traditional grammar, a cardinal numeral (or cardinal number word) is a part of speech used to count. Examples in English are the words one, two, three, and the compounds three hundred [and] forty-two and nine hundred [and] sixty. Cardinal numerals are classified as definite, and are related to ordinal numbers, such as the English first, second, third, etc.[1][2][3]

See also[edit]

  • Arity
  • Cardinal number for the related usage in mathematics
  • English numerals (in particular the Cardinal numbers section)
  • Distributive number
  • Multiplier
  • Numeral for examples of number systems
  • Ordinal number
  • Valency

References[edit]

Notes

  1. ^ David Crystal (2011). Dictionary of Linguistics and Phonetics (6th ed.). John Wiley & Sons. p. 65. ISBN 978-1-405-15296-9.
  2. ^ Hadumo Bussmann (1999). Routledge Dictionary of Language and Linguistics. Taylor & Francis. ISBN 978-0-415-20319-7.
  3. ^ James R. Hurford (1994). Grammar: A Student’s Guide. Cambridge University Press. pp. 23–24. ISBN 978-0-521-45627-2.
Источник

Cardinal Number

Cardinal numbers are numbers that are used for counting. They are also known as natural numbers or cardinals. A set of cardinal numbers starts from 1 and it goes on up to infinity. We use cardinal numbers to answer the question «how many?». For example, how many students are going to the school picnic? The answer could be any number like 20, 23, 30, etc. So, all these numbers come in the category of cardinal numbers. In this article, we will explore the world of cardinal numbers and understand the difference between cardinal and ordinal numbers.

1. What are Cardinal Numbers?
2. Difference Between Cardinal and Ordinal Numbers
3. List of Cardinal Numbers from 1 to 100
4. Cardinal Numbers of a Set
5. FAQs on Cardinal Numbers

What are Cardinal Numbers?

A cardinal number describes or represents how many of something are present. Example 2 apples, 5 flowers, etc. It quantifies an object. It does not have values as fractions or decimals. Cardinal numbers are counting numbers, they help to count the number of items. Let’s have a look at cardinal numbers examples. Ana wants to count the number of people standing in a queue at a billing counter. Can you help her? Ana started to count using Natural numbers.

Cardinal Number Example

Ana counted 1, 2, 3, 4, and 5. There are 5 people standing in a queue at the billing counter. Counting numbers are cardinal numbers! Now, Let’s consider another example, Noah kept eight apples in a basket. The number eight denotes how many apples are there in the basket, irrespective of their order.

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, 21, and so on. The smallest cardinal number is 1 as 0 is not used for counting, so it is not a cardinal number.

Difference Between Cardinal and Ordinal Numbers

All the natural numbers are also referred to as cardinal numbers. Cardinal numbers are used for counting. While an ordinal number is a number that denotes the position or place of an object. Example: 1st, 2nd, 3rd, 4th, 5th, etc. Ordinal numbers are used for ranking. Here is an example that explains cardinal and ordinal numbers:

Cardinal number vs Ordinal number

In the above image, we can see a team of 4 workers on the construction site. This is an example of cardinal numbers.

Difference between Cardinal and Ordinal Numbers

In the above image, we can see the position of the runners in the running event. First, second, third, and so on. This is an example of ordinal numbers. Let’s discuss ordinal and cardinal number differences in the table below:

Cardinal Numbers Ordinal Numbers
They are counting numbers that represent quantity. They are based on the rank or position of an object in a given list or order.
Cardinal numbers give us the answer of ‘how many?’. Ordinal numbers give us the answer of ‘where’. For instance, where does the object lies in the list?
Examples are 1, 2, 3, 4, 5, 10, etc. Examples are 1st, 2nd, 3rd, 4th, 5th, 10th, etc.

List of Cardinal Numbers from 1 to 100

Given below are the basic and most important cardinal numbers, which form the base for other counting numbers.

1 — One 6 — Six
2 — Two 7 — Seven
3 — Three 8 — Eight
4 — Four 9 — Nine
5 — Five 10 — Ten
10 — Ten 60 — Sixty
20 — Twenty 70 — Seventy
30 — Thirty 80 — Eighty
40 — Forty 90 — Ninety
50 — Fifty 100 — Hundred

Given below is the list of all cardinal numbers from 1 to 100. It will also help you to see how we write cardinal numbers in words like 21- twenty-one.

Cardinal Numbers from 1 to 100

Cardinal Numbers of a Set

In the case of a set, the cardinal number is the total number of elements present in it. In other words, the number of distinct elements present in a set is the cardinal number of the set. The cardinal number of a set A is represented as n(A). For example, the cardinal number of set W = {1, 3, 5, 7, 9} is n(W)=5, as there are 5 elements in it.

Think Tank:

  • Maria wrote January 1, 2020, as today’s date in her notebook. Does the number 1 in the date, represent a cardinal number?
  • There are _______ people in the line ahead of me. I am the 7th person in the line.

Important Notes:

  • Cardinal numbers help us to count the number of things or people in or around a place or a group.
  • The collection of all the ordinal numbers can be denoted by the cardinal.
  • Cardinal numbers can be written as words such as one, two, three, etc.
  • Cardinal numbers tell how many items, whereas ordinal numbers show position or ranking.

Related Articles

Check out these interesting articles to know more about cardinal numbers and its related articles.

  • Ordinal Numbers
  • Whole Numbers
  • Natural Numbers
  • Difference Between Natural and Whole Numbers

FAQs on Cardinal Numbers

What is a Cardinal Number Example?

Cardinal numbers are used for counting. Some examples of cardinal numbers are 1, 2, 3, 4, 5, 10, 15, 20, 30, 40, 50, 100, etc. In our daily life, we use cardinal numbers a lot. Even a small child uses this mathematical concept without knowing the term for it. They do count how many toys they have, how many people are there around them, how many friends they have, how many subjects do they study at school, etc.

What is the Smallest Cardinal Number?

The smallest cardinal number is 1 (one) as whenever we count, we always start from 1.

How do you Find Cardinal Numbers?

Cardinal numbers can be found by counting. We start by 1 and then go on as per the number sequence.

How is Cardinal Number Different from the Ordinal Number?

Cardinal numbers are numbers that represent the number of items(quantity) while ordinal numbers represent the rank or position of an item in the given list.

What is a Cardinal Number in Sets?

In set A, if there are a total of 25 elements then 25 is the cardinal number of set A represented by n(A).

Can Cardinal Numbers Negative?

No, cardinal numbers cannot be negative. They are positive integers or natural numbers, as we always count the number of items starting from number 1, and then it goes up to infinity.

Is Zero a Cardinal Number?

No, 0 is not a cardinal number as cardinal numbers represent quantity, and 0 means nothing or no quantity.

What is the Biggest Cardinal Number?

There are infinite natural numbers. Therefore, there are as many cardinal numbers as natural numbers. There can be no generalization of the biggest natural number and so does for the biggest cardinal number.

Источник

What is a cardinal number?

It is a number we use for counting. We need cardinal numbers to say how many objects there are.

Examples of cardinal numbers

They have two children.

There are five oranges in the bowl.

I’ve had three Zoom meetings today.

Numbers from 1 to 12

You’ll have to memorise these numbers.

Number Word
1

one
2

two
3

three
4

four
5

five
6

six
7

seven
8

eight
9

nine
10

ten
11

eleven
12

twelve

Numbers from 13 to 19

All these numbers end with -teen. Don’t forget to stress the last syllable!

Number Word
13

thirteen
14

fourteen
15

fifteen
16

sixteen
17

seventeen
18

eighteen
19

nineteen

Numbers from 20 to 99

All round tens end with -ty. Here is the list.

Number Word
20

twenty
30

thirty
40

forty
50

fifty
60

sixty
70

seventy
80

eighty
90

ninety

To make a compound number, we add 1–9 to round tens with a hyphen..

Examples

21 → twenty-one

46 → forty-six

99 → ninety-nine

Numbers larger than 100

Number Word
100

one hundred (a hundred)
1,000

one thousand
1,000,000

one million
1,000,000,000

one billion

Milliard or billion?

The word «billion» means a thousand million (9 zeros) and it originally came from the US. The British word for «billion» is «milliard» but the British officially accepted the US practice in 1974. Today, you will rarely hear the word «milliard» from a British English speaker. The US terminology for numbers gradually spread from international commerce to everyday life.

Now, let’s look at large compound numbers. To make 3-digit compound numbers, we put and after hundred. See the examples below.

Examples

101 → one hundred and one

110 → one hundred and ten

186 → one hundred and eighty-six

273 → two hundred and seventy-three

750 → seven hundred and fifty

999 → nine hundred and ninety-nine

Pay attention

In US English and is not used. For example, one hundred eighty-six, two hundred seventy-three etc.

With larger numbers, the principle is the same: going from left to right, we say how many thousands, hundreds, tens and ones there are. Note that we do not add and after thousand, million, billion etc.

numbers

Examples

1,304 → one thousand three hundred and four

17,721 → seventeen thousand seven hundred and twenty-one

358,842 → three hundred and fifty-eight thousand eight hundred and forty-two

1,609,100 → one million six hundred and nine thousand one hundred

In writing, we usually put commas after every 3 digits counting from the right. It makes reading simpler.

Pay attention

When pronouncing cardinal numbers, we do not put the words «hundred», «thousand», «million», «billion» into the plural form. Note that there is no -s at the end.

However, when we refer to large but not exact quantities of people, animals or things, we can use these words in plural.

Compare

Thousands of birds were circling over the rocks.

The candidate received two thousand two hundred and fifteen voices.

Zero and synonyms

The symbol 0 or the absence of number is called differently depending on where we use it. You may always use the word zero and people will understand you correctly. However, here is a helpful table in case you come across one of these words, in speaking or writing.

Word Usage Example Reading

o, oh

 in a sequence of digits, e.g. telephone numbers My number is 609 035. My number is six oh nine oh three five

nought

 symbol 0 in British English -2 + 2 = 0 Minus two plus two equals nought.

zero

 symbol 0 in US English;
in Br English — used with temperatures		 -15ºC fifteen degrees below zero

nil, love

 score 0 in various sports (tennis) The score is 40:0. The score is forty love.
Источник

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 go 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.
or
Cardinals mean “how much” exists in a group.

For example, if we want to count the number of apples present in the basket, we 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.

 Table of Contents:

  • Definition
    • Examples
  • Cardinal numbers in English
  • List of Cardinal Numbers
    • Cardinals – Multiples of 10
    • Cardinals – 100 to 1000
  • Cardinal numbers of set
  • Cardinality
  • Cardinal and ordinal numbers
    • Nominal numbers
  • FAQs

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 given numbers, 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 its order. It defines the measure of the size of a set but does not take account of the order.

The set of finite numbers is 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 as we write numbers in words. For the first 10 numbers, we can write as,

  • 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 Numbers 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 purposes They are used to denote the 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 number, 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

Video Lesson on Numbers

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

Q1

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.

Q2

How is a cardinal number different from an ordinal number?

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

Q3

What is the nominal number?

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

Q4

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

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

Q5

Which is the smallest cardinal number?

The smallest cardinal number is 1.

Источник

Cardinal number definition: A cardinal number is a number that expresses how many of a particular item exists.

Ordinal number definition: An ordinal number is a number that expresses a position relative to others.

What is a Cardinal Number?

Cardinal numbers are simply numbers. Cardinal numbers tell us how much of a certain quantity there is.

Examples of Cardinal Numbers:

  • 1
  • 18
  • 23
  • 877
  • 59

What is cardinal data and ordinal dataExamples of Cardinal Numbers:

  • one
  • eighteen
  • twenty-three
  • eight hundred seventy-seven
  • fifty-nine

Examples of Cardinal Numbers in Sentences:

  • I purchased one apple.
  • They ordered 18 sandwiches.
  • He wore the number 23.
  • I think there are 877 jellybeans in the jar.
  • My dad turns 59 this year.

What is an Ordinal Number?

Ordinal numbers are numbers that tell a particular position or place.

What are ordinal numbers Examples of Cardinal Numbers:

  • 1st
  • 3rd
  • 7th
  • 33rd
  • 100th

Examples of Ordinal Numbers:

  • first
  • third
  • seventh
  • thirty-third
  • one hundredth

Examples of Ordinal Numbers in Sentences:

  • The pig placed first at the county fair.
  • She celebrated her third birthday
  • Sam is my seventh pet.
  • Our school is thirty-third in the state.
  • It is the one hundredth anniversary of our city’s founding.

Spelling Numbers Out

What are cardinal numbers The only cardinal numbers that should be written out—not abbreviated with a number—are the numbers one through nine. This is in accordance with AP Style, which is widely held by writers, news publications, journalists, etc.

All other cardinal numbers should be written numerically.

Examples:

  • Correct: We have one dog.
    • Incorrect: We have 1 dog.
  • Correct: You need three pencils
    • Incorrect: You need 3 pencils.
  • Correct: Please buy 40 cups.
    • Incorrect: Please buy forty cups.
  • Correct: She had 11 items on her list.
    • Incorrect: She had eleven items on her list.

All ordinal numbers should be spelled out in writing, not abbreviated.

  • Correct: The team took second place.
    • Incorrect: The team took 2nd place.
  • Correct: They gave a medal to the fourth finisher.
    • Incorrect: They gave a medal to the 4th finisher.

Of course there is nothing grammatical wrong with spelling out larger numbers or using figures for those under 10. These are simply the most conventions across all types of English.

When Is It Okay to Use Figures?

What is cardinal number Sometimes it is acceptable to use a figure (number) instead of writing out the word. Those exceptions are detailed below.

Addresses

A street address requires a number. Therefore, it is acceptable to use a figure instead of writing out the word.

Examples:

  • 1234 Ash Street
  • My grandmother lives at 77 Rocky Lane.
  • Her address is 5688 Tree Trail.

Ages

It is acceptable to use a figure when writing an age.

Examples:

  • I have an 8-year-old cousin.
  • I don’t remember life as a one-year-old.

Proper Names, Proper Nouns

Proper names and proper nouns can use a figure instead of the fully written word.

Examples:

  • Let’s take Highway 1.
  • The fastest route to Washington is Interstate 5.
  • 88 freeway

Millions, Billions, Trillions

Large numbers should be written in a particular format.

Examples:

  • Correct: $5 million
    • Incorrect: five million dollars
  • Correct: The Smith family is worth $2.1 billion.
    • Incorrect: The Smith family is worth two point one billion dollars.
  • Correct: What do you think $1 trillion looks like?
    • Incorrect: What do you think one trillion dollars looks like?

NOTE: Do not ever begin a sentence with a figure. If you must begin a sentence with a number, write out that number. Starting numbers with figures is unacceptable.

  • 500 jobs were created as a result of the tax measure. (Incorrect)
  • Five hundred jobs were created as a result of the tax measure. (Correct)

Figures, however, will occasionally begin a headline.

Summary

Define cardinal numbers: cardinal numbers are numbers denoting quantity.

Define ordinal numbers: ordinal numbers are numbers denoting an item’s place in a series.

In summary,

  • Cardinal numbers are numbers that represent how many of something someone has.
  • These are numbers like one, two, three, and four.
  • Ordinal numbers are numbers that represent place or position.
  • These are numbers like first, second, third, and fourth.

Both ordinal and cardinal numbers follow particular writing rules.

Contents

  • 1 What is a Cardinal Number?
  • 2 What is an Ordinal Number?
  • 3 Spelling Numbers Out
  • 4 When Is It Okay to Use Figures?
    • 4.1 Addresses
    • 4.2 Ages
    • 4.3 Proper Names, Proper Nouns
    • 4.4 Millions, Billions, Trillions
  • 5 Summary

Источник

Topic Index

  1. What is a Cardinal Number?
  2. What is the Cardinal Number of a Set?
  3. List of Cardinal Numbers
  4. Difference Between Cardinal Numbers and Ordinal Numbers?
  5. What is Cardinality?
  6. Cardinal Numbers Example

The cardinal numbers are the numbers that are used for simple counting and that indicates the number of elements present. These are also said to be cardinals. The cardinal numbers are the counting numbers that start from 1 and increase sequentially and are not fractions.

Example: 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25…∞

What is a Cardinal Number?

The quantity of a certain number is represented by a cardinal number. Suppose, I have five flowers in my bouquet. Therefore, we must count those numbers as 1, 2, 3, 4, and 5 in order to get the quantity.

What is the Cardinal Number of a Set?

A number of members present in a set is the Cardinal number of a set. Basically, it shows the count of elements of a particular set.

For example: A{1,2,3,4,5} = 5

Or A{2,7,9,6,8,1,5} = 7

As a result, the only formula for counting numbers is to determine how many elements there are in any set.

List of Cardinal Numbers

1 = One 10 = Ten 100 = Hundred 1000 = Thousand
2 = Two 20 = Twenty 200 = Two Hundred 2000 = Two Thousand
3 = Three 30 = Thirty 300 = Three Hundred 3000 = Three Thousand
4 = Four 40 = Fourty 400 = Four Hundred 4000 = Four Thousand
5 = Five 50 = Fifty 500 = Five Hundred 5000 = Five Thousand
6 = Six 60 = Sixty 600 = Six Hundred 6000 = Six Thousand
7 = Seven 70 = Seventy 700 = Seven Hundred 7000 = Seven Thousand
8 = Eight 80 = Eighty 800 = Eight Hundred 8000 = Eight Thousand
9 = Nine 90 = Ninety 900 = Nine Hundred 9000 = Nine Thousand

The number of Cardinals which are mentioned above is not a limit. There are infinite numbers of cardinal numbers.

Difference Between Cardinal Numbers and Ordinal Numbers?

A cardinal number is a number that expresses the quantity of an item, such as 1, 2, 3, 4, or 5. A number that indicates a particular item’s position in a list, such as first, second, third, fourth, or fifth, is known as an ordinal number.

What is Cardinality?

The number of cardinal members of a set is referred to as cardinality. A non-negative integer can have a limited or infinite degree of cardinality.

Important Points:

  1. Words like one, two, three, etc. can be used to represent the cardinal numbers.
  2. While ordinal numbers indicate position or ranking, cardinal numbers indicate the quantity of elements.
  3. The terms “counting numbers” and “natural numbers” are also used to refer to Cardinal numbers.
  4. Decimal and fractions numbers are not cardinal numbers.
  5. Zero (0) has no meaning, it is not a cardinal number.

Cardinal Numbers Example

  • Five people are standing in a queue as shown 1, 2nd, 3, Four, 5th. Identify the cardinal numbers.

Solution: 1, 3 and Four help us in counting, whereas 2nd, and 5th helps us in identifying the position. Thus, 1, 3, and four are cardinal numbers.

Frequently Asked Questions

1. What are Cardinal Directions?

Ans: The cardinal directions are represented by the four primary points of a compass: north, south, east, and west. N, S, E, and W are also used to refer to them by their first letters.

2. What is an Ordinal Number?

Ans: A number indicating an item’s position in an ordered sequence, such as first, second, or third called Ordinal Number.

3. Is 0 a Cardinal Number?

Ans: No, 0 is not a cardinal number.

Источник

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PRONUNCIATION OF CARDINAL NUMBER

GRAMMATICAL CATEGORY OF CARDINAL NUMBER

Cardinal number is a noun.

A noun is a type of word the meaning of which determines reality. Nouns provide the names for all things: people, objects, sensations, feelings, etc.

WHAT DOES CARDINAL NUMBER MEAN IN ENGLISH?

Cardinal number

In mathematics, cardinal numbers, or cardinals for short, are a generalization of the natural numbers used to measure the cardinality of sets. The cardinality of a finite set is a natural number – the number of elements in the set. The transfinite cardinal numbers describe the sizes of infinite sets. Cardinality is defined in terms of bijective functions. Two sets have the same cardinality if and only if there is a bijection between them. In the case of finite sets, this agrees with the intuitive notion of size. In the case of infinite sets, the behavior is more complex. A fundamental theorem due to Georg Cantor shows that it is possible for infinite sets to have different cardinalities, and in particular the cardinality of the set of real numbers is greater than the cardinality of the set of natural numbers. It is also possible for a proper subset of an infinite set to have the same cardinality as the original set, something that cannot happen with proper subsets of finite sets. There is a transfinite sequence of cardinal numbers: This sequence starts with the natural numbers including zero, which are followed by the aleph numbers.


Definition of cardinal number in the English dictionary

The definition of cardinal number in the dictionary is a number denoting quantity but not order in a set Sometimes shortened to: cardinal. Other definition of cardinal number is a particular number having this function.

Synonyms and antonyms of cardinal number in the English dictionary of synonyms

Translation of «cardinal number» into 25 languages

online translator

TRANSLATION OF CARDINAL NUMBER

Find out the translation of cardinal number to 25 languages with our English multilingual translator.

The translations of cardinal number from English to other languages presented in this section have been obtained through automatic statistical translation; where the essential translation unit is the word «cardinal number» in English.

Translator English — Chinese


基数

1,325 millions of speakers

Translator English — Spanish


número cardinal

570 millions of speakers

Translator English — Hindi


कार्डिनल संख्या

380 millions of speakers

Translator English — Arabic


الكاردينال عدد

280 millions of speakers

Translator English — Russian


количественное числительное

278 millions of speakers

Translator English — Portuguese


número cardinal

270 millions of speakers

Translator English — Bengali


অঙ্কবাচক সংখ্যা

260 millions of speakers

Translator English — French


nombre cardinal

220 millions of speakers

Translator English — Malay


Nombor kardinal

190 millions of speakers

Translator English — German


Kardinalzahl

180 millions of speakers

Translator English — Japanese


基数

130 millions of speakers

Translator English — Korean


기수

85 millions of speakers

Translator English — Javanese


Nomer kardinal

85 millions of speakers

Translator English — Vietnamese


bảng số

80 millions of speakers

Translator English — Tamil


கார்டினல் எண்

75 millions of speakers

Translator English — Marathi


मुख्य क्रमांक

75 millions of speakers

Translator English — Turkish


asıl sayı

70 millions of speakers

Translator English — Italian


numero cardinale

65 millions of speakers

Translator English — Polish


Numer kardynał

50 millions of speakers

Translator English — Ukrainian


кількісний числівник

40 millions of speakers

Translator English — Romanian


număr cardinal

30 millions of speakers

Translator English — Greek


απόλυτος αριθμός

15 millions of speakers

Translator English — Afrikaans


kardinale getal

14 millions of speakers

Translator English — Swedish


kardinalnummer

10 millions of speakers

Translator English — Norwegian


kardinaltall

5 millions of speakers

Trends of use of cardinal number

TENDENCIES OF USE OF THE TERM «CARDINAL NUMBER»

The term «cardinal number» is regularly used and occupies the 92.145 position in our list of most widely used terms in the English dictionary.

Trends

The map shown above gives the frequency of use of the term «cardinal number» in the different countries.

Principal search tendencies and common uses of cardinal number

List of principal searches undertaken by users to access our English online dictionary and most widely used expressions with the word «cardinal number».

FREQUENCY OF USE OF THE TERM «CARDINAL NUMBER» OVER TIME

The graph expresses the annual evolution of the frequency of use of the word «cardinal number» during the past 500 years. Its implementation is based on analysing how often the term «cardinal number» appears in digitalised printed sources in English between the year 1500 and the present day.

Examples of use in the English literature, quotes and news about cardinal number

10 ENGLISH BOOKS RELATING TO «CARDINAL NUMBER»

Discover the use of cardinal number in the following bibliographical selection. Books relating to cardinal number and brief extracts from same to provide context of its use in English literature.

1

Set Theory and Metric Spaces

We are ready for the general definition. DEFINITION. Let d and e be nonzero
cardinal numbers. Let D and E be sets with o(/>) = d, o(E) = e. We define d* to be
the cardinal number of the set of all functions from E to D. Remark: We have …

2

Introduction to Cardinal Arithmetic

Therefore we get Since obviously the cardinality of the index set is at most the
supremum of the summands, Lemma 1.6.3 says that ^<5>^=suP{K^:£</?}<K^. €</
3 Definition Assume that k is an infinite and A is an uncountable cardinal number.

Michael Holz, Karsten Steffens, E. Weitz, 2009

3

An Introduction to Analysis

For this reason, and for others to be elucidated shortly (see Problem D), it is
customary to write 2card* for the cardinal number of the power class on an
arbitrary set X. Thus, in particular, 2N° is the cardinal number of the power class
on N. This …

Arlen Brown, Carl M. Pearcy, 1995

The cardinal number (or cardinality) of a set A, denoted |A|, is the equivalence
class of A under the equivalence relation of equipollence. A is an infinite or finite
cardinal according as A is an infinite or finite set. Cardinal numbers will also be …

Thomas W. Hungerford, 1974

5

The Child’s Understanding of Number

Nor do we assume that a child who uses the counting procedure to establish
such a representation has a full appreciation of all the properties of cardinal
number. There are several set-theoretic definitions of cardinal number, which we
will …

Rochel GELMAN, C. R. Gallistel, Rochel Gelman, 2009

Every finite class has a finite cardinal number, which may be identified with the
number of elements in the class in the ordinary sense; and the finite cardinal
numbers may accordingly be denoted by the symbols 1, 2, . . . . If a finite class is …

Cardinal number of a set The number of elements in a finite set is called the
cardinal number of the set. The cardinal number is used to denote the size of a
set. If A is any finite set, then its cardinal number is denoted by n(A). For example:
If A= …

8

Foundations and Fundamental Concepts of Mathematics

FIGURE 8.5 Definition 3 Two sets that are equivalent are said to have the same
cardinal number. All sets that have the same cardinal number as the set {a} are
said to have cardinal number one (or to contain one element); all sets having the
 …

9

Elements of the Theory of Functions and Functional Analysis

finite sets the concept of cardinal number coincides simply with the concept of
number of elements in the set. The cardinal number of the set of natural numbers
(i.e. of any denumerable set) is denoted by the symbol Ki (read «aleph xero»).

A. N. Kolmogorov, Sergeĭ Vasilʹevich Fomin, S. V. Fomin, 1999

10

Georg Cantor: His Mathematics and Philosophy of the Infinite

managed to establish that the cardinality of Z(K0) was greater than NO, and that
any infinite set of numbers of the second number class was either denumerable ,
or had the cardinal number (a) . The final step was a short one , but he still had to
 …

Joseph Warren Dauben, 1990

10 NEWS ITEMS WHICH INCLUDE THE TERM «CARDINAL NUMBER»

Find out what the national and international press are talking about and how the term cardinal number is used in the context of the following news items.

Baseball Recap: Louisville 7 Carolina 4

The Cardinal number 9 hitter, short stop Devin Hairston, then grounded out to second base to bring up Whiting who struck out to end the inning. «Tar Heel Blog, May 15»

ANSYS’ (ANSS) CEO Jim Cashman on Q1 2015 Results — Earnings …

So, the fact is we’re going to have a revenue ramp up from that; it just won’t count as that to be very cardinal number of numbers in there. «Seeking Alpha, May 15»

Brazilian Actor Wagner Moura Joins “O Magnífico Sete” (The …

Hollywood is continuing the trend of coming up with movie titles using the formula: Definite Article + Adjective + Cardinal Number. This year we … «2paragraphs.com, Apr 15»

All Hail Sam: SFA’s Record Against Their Piney Woods Rival

O-N-E. Definition: “the lowest cardinal number; half of two; 1.” Alright, alright, calm yourselves. Back down Lumberjacks, it’s just one sport – and surely its a fluke. «The Sawmill, Mar 15»

How to Count the Defensive Use of Guns

To the people involved in these incidents, no number of DGUs is more important than the cardinal number representing them. Kleck rose to his … «Reason, Mar 15»

4 Tips for Small Businesses to Decide on a Memorable Brand Name

A few rounds of discussions later at their Stanford University office, they zeroed in on Googol, which is a cardinal number represented as 1 … «Business 2 Community, Feb 15»

No Man’s Sky — The Game We’ll Be Showing Our Grandkids!

Let’s take a look at what that means: A cardinal number represented in the U.S. by 1 followed by 18 zeros, and in Great Britain by 1 followed by … «moviepilot.com, Jan 15»

11 words that mean something completely different at The University …

What is means everywhere else: a cardinal number. What it means at the University of Alabama: Number of national college football … «AL.com, Sep 14»

5 Annual award for American journalism, literature or music (8,5)

… 14 Brave guy (4); 15 Plan (6); 16 Roman goddess of the dawn (6); 17 French city on the Loire (6); 19 Illumination (5); 20 Cardinal number (5) … «The Guardian, May 14»

China Spectacles Industry Report, 2013-2015

Nevertheless, given the large cardinal number of Chinese population, there are three to four million Chinese people in need for corrective … «MarketWatch, Feb 14»

REFERENCE

« EDUCALINGO. Cardinal number [online]. Available <https://educalingo.com/en/dic-en/cardinal-number>. Apr 2023 ».

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So, ordinal numbers are formed by adding th to cardinal numbers. … In compound ordinal numbers, only the last component is in ordinal form: twenty-sixth, seventy-fourth. The tens ending in y change the ending to ie: forty — fortieth.

As in Russian, in English there are numbers: cardinal (Cardinal Numerals) — answer the question «How much?» («One», «fourteen», «one hundred and fifty»); Ordinal Numerals — answer the question «Which one?» («First», «fourteenth», «fiftieth»);

What are cardinal numbers in English?

Cardinal numbers from 1 to 100

As in the Russian language, in English there are numbers, with the help of which we count something. They are called «quantitative» (cardinal numbers), answer the question «how much?»: One — one, two — two. And there are also numbers that are responsible for the order of something when counting.

How are numbers written in English?

Numerals in English. Numerals

  • one — one two — two …
  • thirteen — thirteen fourteen — fourteen …
  • twenty — twenty thirty — thirty …
  • twenty-one — twenty one thirty-three — thirty three …
  • hundred — one hundred one hundred — one hundred …
  • one hundred sixty-eight — one hundred sixty-eight …
  • thousand — thousand …
  • first — the first

How are ordinal numbers formed in English?

Ordinal numbers in English determine the order of objects when counting and answer the question which? (which, which). They are formed by adding the suffix -th to the cardinal number.

How are cardinal numbers formed?

English cardinal numbers, denoting full hundreds, thousands and millions, are formed using the words hundred ‘one hundred’, thousand ‘thousand’ and million ‘million’, which do not add the ending -s. When polydigital numbers more than 100 are formed, the union and is put before tens and units.

How to read numbers in English?

For the numerator, cardinal numbers are used, and for the denominator, ordinal numbers.

  1. 1/2 — one-half, a half (0.5)
  2. 1/100 — one-hundredth (0.01)
  3. 1/5 — one-fifth.
  4. 1/1000 — one-thousandth.
  5. 2/7 — two-seventh.
  6. 44/73 — forty-four seventy-third.
  7. 27/100 — twenty-seven hundredth.

How are numbers read in English?

Cardinal numbers in English

Number in English Transcription Transfer
1 — one [wʌn] / [wan] one
2 — two [tu:] / [tuy] two
3 — three [θri:] / [sri] three
4 — four [fɔ:] / [foo] four

How are complex numbers written in English?

Composite numbers from 20 to 100 are formed in the same way as in Russian: 25 — twenty-five, 93 — ninety-three. The numerals hundred, thousand, million do not acquire the ending s as a plural indicator, but if these words perform the function of nouns, i.e.

When are cardinal numbers used?

Quantitative numerals in Russian Words of this group can denote either an abstract number or the number of some objects. For example: Eight plus four would be twelve. Eight days.

What are ordinal numbers?

Ordinal numerals are a class of numeral names that indicate the order of objects when counting. In Russian, ordinal numbers have all the grammatical features of relative adjectives, but they can be composite (starting from the 21st they are written separately: the twenty-first).

How to write a number in an English notebook?

British English

  1. According to the rules of British English, the date is written first, then the month and year. …
  2. Abbreviated writing of the date with cardinal numbers is also used — or writing the date in numbers separated by slashes or periods.

What is a numeral in English?

The numeral is a part of speech that indicates the number or order of objects. Accordingly, English numerals are divided into two groups: cardinal numerals and ordinal numerals.

What is 3 4 in english?

2/3 — two thirds. 3/4 — three fourths. 1/8 — one eighth.

Источник

Introduction

In mathematics, we come across different types of sets of numbers that have their own characteristics. One such type of number is the cardinal numbers. So, what are these numbers and how are they used? Let us find out.

History of Cardinal Numbers

George Cantor in 1874 – 1884 originated set theory and established the concept of the cardinality of a set. According to him, cardinal numbers were infinite sets and they could also be called as transfinite cardinal numbers. Cantor replaced the elementary concept of a number with a derived and abstract one based on sets (for what it is worth, the informal counting conception is closer to his ordinals than to his cardinals, the notions are equivalent in scope in the finite case but diverge dramatically for infinities). Another mathematician, Traski in 1924 proposed that every set has an association with a cardinal number. Two other mathematicians, Dana Scott and A P Morse later gave the definition of cardinal numbers by considering a set and calling the magnitude of a set as cardinality. 

What are Cardinal Numbers?

Cardinal numbers are the numbers that are used as counting numbers. In other words, the numbers that we use for counting are called cardinal numbers. Another name by which cardinal numbers are known as is natural numbers. In fact, cardinal numbers are the generalisation of natural numbers. The word “ Cardinal” means “how many” of anything is existing in a group. Like if we want to count the number of oranges that are present in the basket, we will have to make use of these numbers, such as 1, 2, 3, 4, 5….and so on.  Let us understand the cardinal numbers by an example.

Suppose we want to tell how many students are present in the class. The answer could be any number such as 8, 20, 45 and so on. These numbers that tell the count of the number of students present in the class are cardinal numbers. Some other examples of cardinal numbers are – 

  1. There are 6 clothes in the bag.
  2. 3 cars are driving in a lane.
  3. Peter has 2 dogs and 1 cat as pets in his house.

In the above three examples, the numbers 6, 3, 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.

How are Cardinal Numbers Represented in English?

We now know that Cardinal numbers define how many things or people are there, for example, five women standing under a tree. In this sentence, the word “five “ represents the cardinal number “ 5 “. 

How many Cardinal Numbers are there?

Since we know that cardinal numbers are used as counting numbers and counting can be of less number of things or more number of things, therefore, this means that there is no end to the list of cardinal numbers. In other words, the number of cardinal numbers is infinite. But an important point to note here is that although the counting of numbers can go on to infinity, but the digits that are used to count the numbers are fixed. In fact, there are only 10 digits that are used for counting of numbers or we can say to represent cardinal numbers. These 10 digits are 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.  It is just the combination of these numbers which make different cardinal numbers such as 36, 43, 75, 89 and so on. The order of these numbers is called counting of numbers. 

This means that the cardinal numbers, since being used as counting numbers are used in the order, 1 ,2 , 3 , 4 , 5 , 6 , 7 , 8 , 9. After 9, the numbers are formed in two digits i.e. the cardinal numbers after 9 will be 1 0, 1 1, 1 2, 1 3 , 1 4 , 1 5 , 1 6 , 1 7 , 1 8 , 1 9. It can be clearly seen here that the digit in tens place remains constant while the digit in one place follows the series. Once the series in one’s place reaches the end, i.e. it reaches 9, the digit in ten’s place is changed to a number of higher-order and the pattern is followed. Therefore, after 1 9 we will have 2 0 , 2 1 , 2 2 and so on.  After all the numbers in two digits are over, three-digit numbers are followed. The three-digit number starts from 100 and goes on till 999. Three-digit numbers are followed by four-digit numbers and so on. Therefore, there is no limit to the cardinal numbers which means cardinal numbers are infinite. 

Cardinal Numbers From 1 to 100

Below is the list of cardinal numbers from 1 to 100

Nominal Number – Cardinal Number Nominal Number – Cardinal Number Nominal Number – Cardinal Number Nominal Number – Cardinal Number
1 One 2 6 Twenty Six 5 1 Fifty One 7 6 Seventy Six
2 Two 2 7 Twenty Seven 5 2 Fifty Two 7 7 Seventy Seven
3 Three 2 8 Twenty Eight 5 3 Fifty Three 7 8 Seventy Eight
4 Four 2 9 Twenty Nine 5 4 Fifty Four 7 9 Seventy Nine
5 Five 3 0 Thirty 5 5 Fifty Five 8 0 Eighty
6 Six 3 1 Thirty One 5 6 Fifty Six 8 1 Eighty One
7 Seven 3 2 Thirty two 5 7 Fifty Seven 8 2 Eighty Two
8 Eight 3 3 Thirty Three 5 8 Fifty Eight 8 3 Eighty Three
9 Nine 3 4 Thirty Four 5 9 Fifty Nine 8 4 Eighty Four
1 0 Ten 3 5 Thirty Five 6 0 Sixty 8 5 Eighty Five
1 1 Eleven 3 6 Thirty Six 6 1 Sixty One 8 6 Eighty Six
1 2 Twelve 3 7 Thirty Seven 6 2 Sixty Two 8 7 Eighty Seven
1 3 Thirteen 3 8 Thirty Eight 6 3 Sixty Three 8 8 Eighty Eight
1 4 Fourteen 3 9 Thirty Nine 6 4 Sixty Four 8 9 Eighty Nine
1 5 Fifteen 4 0 Forty 6 5 Sixty Five 9 0 Ninety
1 6  Sixteen 4 1 Forty One 6 6 Sixty Six 9 1 Ninety One
1 7 Seventeen 4 2 Forty Two 6 7 Sixty Seven 9 2 Ninety Two
1 8 Eighteen 4 3 Forty Three 6 8 Sixty Eight 9 3 Ninety Three
1 9 Nineteen 4 4 Forty Four 6 9 Sixty Nine 9 4 Ninety Four
2 0 Twenty 4 5 Forty Five 7 0 Seventy 9 5 Ninety Five
2 1 Twenty One 4 6 Forty Six 7 1 Seventy One 9 6 Ninety Six
2 2 Twenty Two 4 7 Forty Seven 7 2 Seventy Two 9 7 Ninety Seven
2 3 Twenty Three 4 8 Forty Eight 7 3 Seventy Three 9 8 Ninety Eight
2 4 Twenty Four 4 9 Forty Nine 7 4 Seventy Four 9 9 Ninety Nine
2 5 Twenty Five 5 0 Fifty 7 5 Seventy Five 100 One Hundred

Properties of Cardinal Numbers

Following are the properties of cardinal numbers – 

  1. Cardinal numbers help us to count the number of things or people in or around a place or a group.
  2. The collection of all the ordinal numbers can be denoted by the cardinal.
  3. Cardinal numbers can be written as words such as one, two, three, etc.
  4. Cardinal numbers define the measure of the size of a set but do not take account of the order.
  5. Cardinal numbers are also called counting numbers and natural numbers
  6. A group of ordinal numbers can be represented by cardinal numbers
  7. Cardinal numbers are always used to count and are stated by ‘how many’
  8. Fractions and decimals are not cardinal numbers
  9. Zero (0) is not a cardinal number, since it means nothing
  10. The cardinality of a set represents how many objects or elements are there in the set

As we know that there are other types of sets as well that possesses their own properties. For example, apart from cardinal numbers, there are two other numbers that are ordinal numbers and nominal numbers. So, how similar are cardinal numbers with ordinal numbers and nominal numbers? Or, rather how different all the three types of numbers are from each other. Let us find out.

Nominal numbers are numbers in numeric form. For instance, 25 is the nominal number for the number “ Twenty Five “. Hence, the nominal numbers and cardinal numbers are different representations of the same numbers. We can also say that the nominal numbers are another type of number, different from cardinals and ordinals, used to name an object or a thing in a set of groups. They are used for the identification of something. It is not for representing the quantity or the position of an object.

Ordinal number describes the position of things. In other words, an ordinal number is a number that denotes the position or place of an object. For example, 1 st, 2 nd, 3 rd etc. are all ordinal numbers. Ordinal numbers are used for the purpose of ranking. 

Let us compare cardinal numbers vs ordinal numbers

Cardinal Numbers vs Ordinal Numbers

Let us consider an example. Suppose in a race there were 10 athletes who participated. The athlete who came first was awarded a gold medal, while a silver medal was given to the candidate who stood second and a bronze medal was given to the athlete who came third. In this case, the number 10 which represents the number of athletes that participated in the race is the cardinal number. On the other hand, the positions first ( 1 st ), second (2 nd ) and third (3 rd ) are ordinal numbers as they represent the position. 

Let us summarise the difference between cardinal numbers and ordinal numbers

Cardinal Numbers Ordinal Numbers
Cardinal Numbers are counting numbers that represent quantity. Ordinal Numbers are based on the rank or position of an object in a given list or order.
Cardinal numbers give us the answer of ‘how many?’ Ordinal numbers give us the answer of ‘where’. For instance, where does the student position in the list?
Examples of cardinal numbers are 1 , 5 , 8 , 20 , 35 etc. Examples of ordinal numbers are 1 st, 2 nd, 3 rd etc.

Let us now compare some cardinal numbers with their nominal numbers and ordinal counterparts

Cardinals Ordinals
1 One 1st First
2 Two 2nd Second
3 Three 3rd Third
4 Four 4th Fourth
5 Five 5th Fifth
6 Six 6th Sixth
7 Seven 7th Seventh
8 Eight 8th Eighth
9 Nine 9th Ninth
1 0 Ten 10th Tenth
1 1 Eleven 11th Eleventh
1 2 Twelve 12th Twelfth 
1 3 Thirteen 13th Thirteenth
1 4 Fourteen 14th Fourteenth
1 5 Fifteen 15th Fifteenth
1 6  Sixteen 16th Sixteenth
1 7 Seventeen 17th Seventeenth
1 8 Eighteen 18th Eighteenth
1 9 Nineteen 19th Nineteenth 
2 0 Twenty 20th Twentieth 

What is Cardinality of a Set?

The cardinality of a group (set) tells how many objects or terms are there in that set or group. In other words, the cardinality of a finite set is a natural number: the number of elements in the set. For example, the set A  = { 1 , 3 , 5 , 7 , 9 } has a cardinality of 3 as there are 3 elements in the set. 

Solved Examples

Example 1 What is the cardinal number of set A = { 3, 5, 7, 9, 10, 11, 4, 19 } ? What is the ordinal number of the number 7 in the set?

Solution We have been given the set A = { 3, 5, 7, 9, 10, 11, 4, 19 }. We need to find

  1. The cardinal number of set A
  2. The ordinal number of the number 7 in the set

Let us find these one by one.

First, let us count the number of elements in the set A.  The total number of elements in the given set is 8.

Therefore, the cardinal number of the set A is 8.

Now, let us check the position of the element 7 in the given set. It is at the third position in the set. 

Therefore, the ordinal number of the number 7 in the set A is 3 rd ( Third ).

Example 2 These are the first 10 English letters given in order. Express them in ordinal numbers as well as cardinal numbers where D is the fourth letter at the number 4 in the set.

  { A,   B,   C,   D,   E,   F,   G,   H,   I,   J }

Solution We have been given the set { A,   B,   C,   D,   E,   F,   G,   H,   I,   J }. It has also been given that D is the fourth letter at the number 4 in the set.

Let us write the ordinal and the cardinal numbers for element of the given set. We will have,

Element of the Set Ordinal Number Carinal Number
A 1st First 1 One
B 2nd Second 2 Two
C 3rd Third 3 Three
D 4th Fourth 4 Four
E 5th Fifth 5 Five
F 6th Sixth 6 Six
G 7th Seventh 7 Seven
H 8th Eighth 8 Eight
I 9th Ninth 9 Nine
J 10th Tenth 1 0 Ten

Key Facts and Summary

  1. Cardinal numbers are the numbers that are used as counting numbers
  2.  Cardinal numbers are the generalisation of natural numbers.
  3. Cardinal numbers help us to count the number of things or people in or around a place or a group.
  4. The collection of all the ordinal numbers can be denoted by the cardinal.
  5. Cardinal numbers can be written as words such as one, two, three, etc.
  6. Cardinal numbers define the measure of the size of a set but do not take account of the order.
  7. Cardinal numbers are also called counting numbers and natural numbers
  8. A group of ordinal numbers can be represented by cardinal numbers
  9. Cardinal numbers are always used to count and are stated by ‘how many’
  10. Fractions and decimals are not cardinal numbers
  11. Zero (0) is not a cardinal number, since it means nothing
  12. Cardinality of a set represents how many objects or elements are there in the set
  13. The nominal numbers and cardinal numbers are different representations of the same numbers.
  14. The number of cardinal numbers is infinite. 
  15. Although the counting of numbers can go on to infinity, but the digits that are used to count the numbers are fixed. In fact, there are only 10 digits that are used for counting of numbers or we can say to represent cardinal numbers.
  16. Ordinal number describes the position of things. In other words, an ordinal number is a number that denotes the position or place of an object. Ordinal numbers are used for the purpose of ranking.
  17. The cardinality of a group (set) tells how many objects or terms are there in that set or group.

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