# Difference between Cardinal, Ordinal, and Nominal Numbers

Arithmetic is an elementary part of the number theory. Arithmetic is a branch of Mathematics, which consists of the study of numbers and traditional operations such as addition, subtraction, multiplication, division, finding roots, exponential, etc. It deals with properties and manipulations of numbers.

### Number and Number System

The number is the most basic unit of mathematics. It is an arithmetic value represented as a word, symbol, figure, etc. Numbers are used for counting, calculations, measuring, etc. Example of numbers: 1, 2, 3, 458, 102556, etc.

• 1, 3, 5, 89, etc. are called odd numbers.
• 2, 4, 6, 8, 10, 1236, etc. are called even numbers.

Number systems are set of symbols that represent numbers. It defines a set of values to represent a quantity. It is basically the representation of numbers by using digits or symbols. There are majorly four types of number systems, they are, binary number system, decimal number system, octal number system, and hexadecimal number system.

### What are the differences between cardinal, ordinal, and nominal numbers?

Cardinal numbers, ordinal numbers, and nominal numbers all are defined for the decimal number system. Cardinal numbers as the name suggests are used for counting. Ordinal numbers are used for arranging different numbers, and nominal numbers are used for identification purposes, for example, a person’s passport number is the nominal number. Let’s take a look at the difference among all three types of numbers,

 Cardinal Numbers Ordinal Numbers Nominal Numbers Cardinal numbers are the numbers that are used for counting. It helps us to know how many elements are there. Ordinal numbers are the concept of natural numbers which is used to describe a way to arrange different elements. Nominal numbers can be defined as numbers that are used for identifications. The smallest cardinal number is 1 and not 0 since 0 is not a counting number. It basically denotes the position of an element with respect to other elements These are used to label items uniquely. Examples of cardinal numbers: 1,2,3,4 …. so on. Examples of ordinal numbers: 1st- first, 2nd- Second, 12th- twelfth etc. Examples of nominal numbers: Passport number, Cell phone number, ZIP code number, etc.

### Sample Problems

Question 1: Which is the smallest cardinal number?

Answer:

1 is the smallest cardinal number.

Question 2: Which of the following is an example of Ordinal Numbers?

1. 123
2. PinCode: 851142
3. Fourth
4. 2568

Answer:

Fourth is the example of an ordinal number.

Question 3: The days of the week are given as follows:

Sunday   Monday   Tuesday   Wednesday   Thursday   Friday   Saturday

• Which is the third day of the week?
• Which is the last or seventh day of the week?

Answer:

• Tuesday is the third day of the week.
• Saturday is the last or seventh day of the week.

Question 4: What is the cardinal number for the set X = {31, 50, 17, 1521, 400, 285819}?

Answer:

Set X contains 6 elements. Therefore, the cardinal number for set X is 6.

Question 5: Which of the following are even numbers?

25,12, 26 289, 20, 22, 86.

Answer:

12, 26, 20, 22, 86 are all even numbers since all these are divisible by 2.

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