Table of Contents

## Numbers and Number System

The Numbers are the mathematical values that are used to calculate, measure, or organize objects. The Number System may be defined as the system for representing a specific group of numbers in a specific way based on some predefined criteria. So, basically, the **Number System** is a system that consists of different sets of numbers.

Examples of a group of numbers in the **Number System** are **Natural Numbers**, **Whole Numbers**, **Integers**, **Rational Numbers**, **Irrational Numbers** etc. There are many other different groups of numbers such as odd, even, complex numbers etc.

However, in this context we are going to learn only about the Natural Numbers, Whole Numbers, Integers, Rational Numbers, Irrational Numbers, Real Numbers etc.

Before proceeding to **Number Systems**, let us first recall about the **Number Line**.

## Number Line

We know that the **Number Line** is a Straight line that is used to place numbers at specific positions as shown in the figure below. The distance between two consecutive numbers in the **Number Line** should be equal.

From the above figure of **Number Line**, 0 is the neutral point. Now, if we move to the Right-Hand-Side of the **Number Line** starting from 0, we will get **Positive Numbers** and similarly, if we move to the Left-Hand-Side of the **Number Line** starting from 0 we will get **Negative Numbers**. If we keep on moving, we will get keep getting bigger numbers on the Right-Hand-Side and Smaller Numbers on the Left-Hand-Side. However, these numbers never finish and keep on increasing up to +\infty or decreasing up to -\infty if we keep moving in the right and left directions respectively.

## Natural Numbers

The set of all the numbers starting from 1 in the Right-hand side of the number line are called the **Natural Numbers**. These numbers start from 1 and ends at +\infty. The **Natural Numbers** are represented by the letter N. The set of **Natural Numbers** can be written as,

N=\{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, …………\}

The representation of **Natural Numbers** in the **Number Line** is shown in the figure below.

## Whole Numbers

The set of numbers that starts from 0 and ends at +\infty is called the **Whole Numbers**. Therefore, the **Whole Numbers** are basically the set of **Natural Numbers** and 0 is included in them. The **Whole Numbers** are represented by the letter W and can be written as,

W=\{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, ………\}

The representation of **Whole Numbers** in the **Number Line** is shown in the figure below.

## Integers

The collection of both the **Whole Numbers** and the **Negative Numbers** are called the **Integers**. Therefore, the set of **Integers** will contain **Positive Numbers**, **Negative Numbers** as well as zero (0) in it. The Natural Numbers, Whole Numbers and 0 are the parts of **Integers**. **Integers** are represented by the letter Z and can be written as,

Z=\{…… , -4, -3, -2, -1, 0, 1, 2, 3, 4, ……\}

The representation of **Integers** in the **Number Line** is shown in the figure below.

Note: The set of **Natural Numbers**, **Whole Numbers** and **Integers** contains whole-valued numbers only. They do not contain fractions or decimals.

## Frequently Asked Questions (FAQ)

### What are Natural Numbers?

The numbers that start from 1 and ends at +∞ are called the Natural Numbers. Natural Numbers are denoted by the letter N and can be represented by,

N={1, 2, 3, 4, 5, 6, 7, …………}

### What are Whole Numbers?

The numbers that start from 0 and end at +∞ are called the whole numbers. Therefore, the set of Whole Numbers is the set of Natural Numbers with 0. The Whole Numbers are denoted by the letter W and can be represented by,

W={0, 1, 2, 3, 4, 5, 6, 7, 8, …………}

### What are Integers?

The collection of whole-valued positive numbers, negative numbers and 0 are called the integers. Integers are denoted by the letter Z and can be represented as,

Z={……… , -4, -3, -2, -1, 0, 1, 2, 3, 4, ……….}

### Is every Natural Number a Whole Number?

Yes, every Natural Number is a Whole Number because the Whole Numbers are the collection of all the Natural Numbers and zero (0).

### Is every Integer a Whole Number?

No, every Integers is not a Whole Number. It is because the set of Integers includes Positive Numbers, Negative Numbers and Zero (0). However, the set of the Whole Number only includes the Positive Numbers and Zero (0).

For Example, -5 is an Integer but not a Whole Number.

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