[Maths Class Notes] on Cardinal Numbers Pdf for Exam

What Are Cardinal Numbers?

Cardinal numbers are the generalization of natural numbers as it consists of all the counting numbers starting from one. Cardinal numbers are also called cardinals. The term cardinal numbers or cardinal was coined to represent the size of a set called cardinality (size) of sets. Cardinality is the number of elements present in a finite set which usually describes the size of the sets. For example, let us take two sets – Set A = {2, 4, 6, 8} and set B = {1, 2, 3, 5, 7}. The cardinality of set A is 4 as there are 4 elements present in set A whereas the number of elements present in set B is 5 so the cardinality of set B is 5. Cardinal tells us how many of something is present such as one, two, three, four, five, etc. 

Apart from cardinal numbers, there are two other numbers that are ordinal and nominal. Cardinal number tells us how many of something is present, ordinal number describes the position of things and nominal number usually represents the name. For example, there were 11 players playing a game where each player has a number printed on the shirt that represents him. Suppose player number 33 comes first. Then, in this case, the cardinal number is 11 because there are a total of eleven players, the ordinal number of the player who won is 1st and the nominal number is 33 as it represents the player who one. 

Summary

• Cardinal Number (How many): 11

• Ordinal Number (Position): 1st

• Nominal Number (Name): 33

How Many Cardinal Numbers are There?

Cardinal numbers are used as counting numbers. Counting can be of less number of things or more number of things. For example, we can count the number of fans in a house, the number of sheep on the farm, the number of hairs in our head, or the number of stars in the sky. All can be counted by using numbers like one, two, three, four, and so on. The counting can go on to infinity but there are a limited number of digits used. Basically there are 10 digits used to represent any number and those digits are 1, 2, 3, 4, 5, 6, 7, 8, 9 and 0. Zero (0) alone is not a cardinal number. But zero can be used with other digits to represent numbers like 10, 20, 30, 700, 9000, etc.  The combination of numbers is used in series 1, 2, 3, 4, 5, 6, 7, 8, 9, 0. Once the number becomes double-digit, we change the ones of the number following the series. Example, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19. Here, the digit in tens place remains constant while the digit in one place follows the series. 

Once the series in one place reaches the end (i.e, 9), the digit in ten’s place is changed to a number of higher-order and the pattern is followed. Example, 20, 21, 22, 23, 24, 25, 26 27, 28, 29. The pattern is followed until one’s reaches 99. 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. 

Solved Examples

Example 1: Show how you can coordinate cardinal numbers with ordinal numbers?

Solution: Cardinal numbers and ordinal numbers can be coordinated as shown below: