Math Concepts

# Numbers

Numbers in some way or the other form the basis of all living beings. The laptops and computers that everyone today can’t seem to live without work based on numbers and only numbers. The use of numbers in every person's day to day life is undebatable since without numbers, we can’t even think of performing typical day to day activities such as counting of things, checking date or time, etc. We should befriend numbers for understanding the world of Mathematics.

 1 Introduction 2 What are Numbers? 3 History/Background of Numbers 4 Types of Numbers 5 Summary 6 FAQS

4th September 2020

## Introduction

As mentioned earlier, Numbers have so vast a scope in mathematics that it can no longer be considered a single topic but rather an amalgamation of many topics and sub-topics. We will see each topic in great detail through this series of blogs.

## What are Numbers?

A Number is an arithmetic value that can represent some quantity and be used in calculations. A symbol like “3”, “5,” or “7,” which is used to represent a number, is known as numerals. A number system is a system for denoting numbers logically using digits or symbols. The numeral system:
Represents a set of numbers
Reflects the arithmetic and algebraic structure of a number
Provides a standard form of representation
While counting things in our life we don’t count everything in English, so here we try to learn various numbering methods used by people around our country

1. Numbers in Hindi

In this blog, we will see numbers from 1-10 written in Hindi.

 Hindi English Number शून्य Shunya (Zero) ० (0) एक Ik (One) १ (1) दो Do (Two) २ (2) तीन Teen (Three) ३ (3) चार Chaar (Four) ४ (4) पाँच Panch (Five) ५ (5) छ: Chhah (Six) ६ (6) सात Saat (Seven) ७ (7) आठ Aath (Eight) ८ (8) नौ Nau (Nine) ९ (9) दस Das (Ten) १० (10)

For further numbers, you can refer here.

 Kannada English Number ಸೊನ್ನೆ Sonnē (Zero) 0 (೦) ಒಂದು Ondu (One) 1 (೧) ಎರಡು Ēraḍu (Two) 2 (೨) ಮೂರು Mūru (Three) 3 (೩) ನಾಲ್ಕು Nālku (Four) 4 (೪) ಅಯ್ದು Aydu (Five) 5 (೫) ಆರು Āru (Six) 6 (೬) ಏಳು Ēḷu (Seven) 7 (೭) ಎಂಟು Ēṇṭu (Eight) 8 (೮) ಒಂಬತ್ತು Ombattu (Nine) 9 (೯) ಹತ್ತು Hattu (Ten) 10 (೧೦)

For further numbers, you can refer here.

## History/Background of Numbers

The Egyptians were the first to invent a ciphered numeral system, and the Greeks followed them by mapping their counting numbers onto the Ionian and Doric alphabets. Roman numerals, a system that uses a combination of letters of the Roman alphabets, remained dominant in Europe until the Hindu–Arabic numeral system spread. The Hindu-Arabic numeral system that came into being around the late 14th century remains the most common system for representing numbers in the world today. The key to the system's effectiveness was the symbol for zero, which was developed by ancient Indian mathematicians around 500 AD.
Many other artifacts have been discovered with marks cut into them that many believe to be tally marks. These tally marks have been used for counting elapsed time, such as the no. of days, no. of lunar cycles, or keeping records of quantities, such as of animals.
A tallying system holds no concept of place value (as in modern decimal notation), limiting its representation of large numbers. Nonetheless, tallying systems are considered to be the first kind of abstract numeral system.
Tally marks, which are also called hash marks, are a unary numeral system. They are a form of numeral that can be used for counting or tallying ongoing results, such as the score in a game or sport, as no intermediate results need to be erased or discarded.
The first known system with place value was the Mesopotamian base 60 system and the earliest available base 10 system dates to 3100 BC in Egypt.

## Types of Numbers

The different types of numbers can be classified into sets: 1. Natural Numbers: Natural numbers, also known as counting numbers, contain the positive integers from 1 up to infinity. The set of natural numbers is denoted by “N”, and includes N = {1, 2, 3, 4, 5, ……….}
2. Whole Numbers: Whole numbers known as non-negative integers do not include any fractional or decimal part in their numbers. The set is denoted by “W,” and the set of whole numbers includes W = {0,1, 2, 3, 4, 5, ……….}
3. Integers: Integers are the set of all whole numbers with the addition of the negative set of natural numbers. “Z” represents integers and the set of integers are Z = { -3, -2, -1, 0, 1, 2, 3}
4. Real Numbers: All positive and negative integers along with fractional and decimal numbers without imaginary numbers, are called real numbers. The symbol “R represents it”.
5. Rational Numbers: Any number written as a ratio of one number over another number is written as rational numbers. This means that any number that can be written in the form of p/q. The symbol “Q” is used to represent the set of rational numbers.
6. Irrational Numbers: The number that cannot be expressed as the ratio of one over another is known as irrational numbers, and it is represented by the symbol ”P”.
7. Complex Numbers: The number that can be written in the form of a+bi where “a and b” are the real number and “i” is imaginary is known as a complex number. The set is represented by “C”.
8. Imaginary Numbers: The imaginary numbers are the complex numbers that can be written in the form of the product of a real number and the imaginary unit “i”

The above types of numbers can be broadly classified into two categories:

1. Countable Numbers
2. Uncountable Numbers

Though the concept of countable and uncountable is more applicable for sets than numbers, we will simplify it in the above-linked blogs.

Countable Sets will include the sets of Natural Numbers, Whole Numbers, and Integers. In contrast, Uncountable Sets will consist of the sets of Rational Numbers, Real Numbers, Irrational Numbers, Imaginary Numbers, and Complex Numbers.

## Summary

Through the course of this blog, we have come to summarize that given the importance of Numbers in Mathematics and our day to day life it is something that we will understand over a course of topics. Numbers and their arithmetic properties are of great importance and need to be studied and practiced a great deal to get a firm understanding and grasp. Numbers will be explored in further topics: Natural Numbers, Real Number, Rational Numbers, etc. and operations on them in another set of topics: PEMDAS, LCM, HCF, etc.

## 1. What are Natural Numbers?

The set of Natural numbers is the set 1, 2, 3, .... One such example can be 5.

## 2. What are Prime Numbers?

Any number that is greater than 1 and has exactly two factors, 1 and itself, is defined as a prime number.

## 3. What are Composite Number?

Any number that is greater than 1 and has more than two factors is defined as a composite number.

## 4. What are Whole Numbers?

Whole numbers are the set of natural numbers (Counting numbers) plus 0.

We use Natural numbers in our everyday life, in counting discrete objects, that is, objects which can be counted.

## 5. What are some of the primary applications of Numbers?

Primary applications of numbers include counting and labeling. Apart from this, numbers are extensively used for calculating various things such as total marks, percentage, etc.

## 6. Where are numbers used most often?

Numbers are mostly used in Mathematics, which also aid in Computer Sciences and almost all other applications based on mathematical calculations.

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