Table of Contents

Why We need Natural Numbers. 2

Why we need Rational Number. 4

Why We Need Irrational Numbers. 5

Why We need Complex Numbers. 7

I don’t want to teach the history of numbers; I just want to tell the readers how a mathematics teacher teaches his students.

### Why do we need numbers?

Why do human beings need numbers? Why do we learn numbers? Why do we need integers, and why do we need imaginary numbers, even if they are imaginary?

So, these thoughts come to the mind of the child and also of the adult, even of the teacher who is teaching math.

Numbers – Definition, Types of Numbers, Charts, Properties, Examples (byjus.com)

### Why do we need Natural Numbers?

A person who is grazing his goats needs numbers to count his goats in the evening. So, naturally, he needs numbers; that’s why he needs counting numbers, or natural numbers, and we already know that natural numbers are 1, 2, 3, 4, ….

**Natural Numbers Definition and Examples**

Children who are living in the United States of America, Canada, India, or Pakistan need 1, 2, 3, … to count the chairs in their class. Oh, I discovered the new definition of mathematics: that math is a religion that is acceptable to all the people in the world.

### Why do we need whole numbers?

When I was teaching mathematics, I was thinking about how I explained whole numbers, so a story came to mind. The word “story” captured the attention of students. They began to look at me and want to listen. Are you astonished? Children want to hear the mathematics teacher’s voice.

A person who was grazing his goats suddenly saw three lions come and attack them. The person ran and climbed a tree. In an hour, all the goats had died. So, he left nothing. So he doesn’t need to count anything, so nothing is actually zero. Whole numbers start from 0.

So whole numbers are 0, 1, 2, 3, 4, …. we need a number to express nothing.

People use this number to alternatively use the word “nothing”. For example, a husband with no IQ can tell his wife, “You have zero talent for cooking.”

A father can use a sentence to insult his son: “You have **zero** participation in the income of our family.”

It is worth mentioning here that all natural numbers are part of whole numbers

As N= {1, 2, 3, 4, ………}

W= {0, 1, 2, 3, 4, ……}

So mathematically, we can write

N **⊆ W**

This means N is a subset of W.

**Why do we need integers?**

Why do we need integers, or is it just a topic to give a headache to children? Is there any use for negative numbers? $5 can be put in your pocket, but what is the meaning of -$5? You have nothing that can be understood, but your negative financial condition cannot be understood.

**Set of integers ={ 0,****±****1, ****±****2, ****±****3, ****±****4,………..} = Z**

Consider an example from life: Stacey has no money; we can say she has zero money. **If Stacey takes a $5 loan from her friend Bush, we can say she has a financial position of -$5.** Similarly, a person has $100, and he spends $20 on the donation, so now the money he left is $100-$20=$80. So, we need negative numbers in our lives. But negative numbers are not too negative; they also have positive uses.

Remember one thing: that set of natural numbers is subset of whole numbers, and both are subsets of integers.

N **⊆ W ⊆ Z**

### Why do we need a Rational Number?

Rational numbers are in fraction form (I will define them later), but why do we need fractions? You use it in your daily life, but you don’t know that you are using fractions.

Your wife said, “Divide the cake in half,” which means 1/2. Divide the pizza into 4 parts, which means one part consists of 1/4 of the pizza.

Consider the diagram

A piece of wood has been cut into 3 parts; if I take 1 part, it means 1/3; if I take 2 parts from the three parts, it means 2/3. Now, we discuss the definition of Rational numbers (please review the integers, which I have written above).

Rational numbers can be written (essential words: “which can be written”) in h/q form, where h and q are both integers and q is not equal to zero.

What is a Rational Number? Definition and Rational Number Example (freecodecamp.org)

Now consider a few examples of Rational Numbers.

Why 5/3 a Rational Number? As 5 and 3 are integers, if the first and ground floors of a house are integers, it means it is a rational number.

Similarly, –7/2 , –8/9 , 2/7 and -15/13 are Rational Numbers examples.

**What are the numerator and denominator, with example?**

It is worth mentioning here that in 5/3, 5 is called the numerator and 3 is called denominator.

Do you know that 8 is a rational number?

How?

Again, look at the definition of rational numbers. It is mentioned that they can be written in h/q form, so 8 can be written in 8/1 form, so that’s why 8 is a rational number. Similarly, 0 is a rational number, as it can be written in the form of 0/1. It means we can say each and every integer is a Rational Number, but each rational number is not an integer.

### Why do we Need Irrational Numbers?

When I told my mathematics class that the __simple definition of irrational numbers is that they are numbers that are not rational numbers__. One of my students said, “7/0 is an irrational number”. I smiled and told him to remember that 7/0 is not a number because no number can be divided by zero.

An example of a Rational number is √2, as it cannot be written in h/n form where h and n are integers and n is not equal to zero.

Use in daily life? You will be astonished to hear that irrational numbers are also used in industry.

Before making any circular shapes, we have to bend the material into a round shape. The question is, if we need a circle with a radius of 2 feet, “How long is the strip?

The formula for the circumference of a circle is 2πr. This magical number π has magical characteristics, and it is an irrational number.

Before discussing more interesting facts about π, you have to understand the concept of the diameter of a circle. Look at the diagram below to understand the diameter of the circle.

C=2πr

If we solve the above equation for π, we get

π = C/2r

π = Circumference /diameter of the circle

This formula reveals the secret of the earth: if you take any circle, big or small, and divide the circumference of a circle by its diameter, you get a magical number π.

### Why do we need complex numbers?

Before discussing complex numbers, you have to understand the concept of the square root. We know that (2)^{2}=4 and (-2)^{2} is also equal to 4. That’s why √4 = ±2.

But is difficult to solve √-4 , as there is no such number whose square gives – 4. So, it’s a huge problem for mathematicians, so this problem has been solved by declaring* i* =√-1

So, √-4 now can be written as 2*i*

Complex Numbers (Definition, Formulas, Examples) (byjus.com)

It is fairly sufficient for me that I have spent over three hours today browsing the internet but have yet to come across an article as fascinating as yours. If only all website owners and bloggers produced high-quality content in the same manner as you, the internet would be considerably more useful than it is now.

Thank you; your comment is a real reward for me.