__Number System__

__Number System__

Since time immemorial, Number and Number System have become an integral part of our life and it has dominated the entire world of Human Civilization in such a way that without it we can’t even imagine the existence of a small creature. So let us know the Number and Number System under various categories.

** NATURAL NUMBER**: Counting of objects/materials for the first time lead to the existence of the numeral

**1(One)**. So, now we are all familiar that in order to count any objects we have to start with the numeral

**1(one**). This numeral

**1(one)**came into existence in a Natural Way. So it is known as Natural Numbers or Counting Numbers.

Hence, the set of numbers which are used in counting objects are called Natural Numbers or Counting Numbers.

N = {1,2,3,4,5,6,7,8,9,10,11,12,13,……….}

As the counting process starts from **1(one),** so we can say that **1(One)** is the smallest Natural Number.

[*Can we write the largest Natural Number? (Think yourself and post a comment in our website)*]

** WHOLE NUMBERS: **The set of numbers which starts from numeral

**0(Zero)**are called Whole Numbers

W = {0,1,2,3,4,5,6,7,8,9,10,11,12,13,……….}

[*Can we write the largest Whole Number? (Think yourself and post a comment on our website)*]

**All Natural Numbers are Whole Numbers, but all Whole Numbers are not Natural Numbers.**

*(Think yourself and post a comment on the box, which Whole Number is not a Natural Number*?)

** INTEGER**: It is a Latin word which means

**Whole**. In general, we can say that the numbers which can be expressed/written without its fractional components are called Integers. For example –

**but**

*9, 12, 13, etc are integers***etc are not integers.**

*9.25, 12.365, 13.5222,*

The Set of Integers can be expressed as

I or Z= {…………,–13, –12, –11, –10, –9, –8, –7, –6, –5, –4, –3,–2, –1, 0, 1,2,3,4,5,6,7,8,9,10,11,12,13,………….}

OR

I or Z = {…………,–13, –12, –11, –10, –9, –8, –7, –6, –5, –4, –3, –2, –1, 0, +1, +2, +3, +4, +5, +6, +7, +8, +9, +10, +11, +12, +13,………..}

Integers are broadly classified into two groups:

- Positive Integers
- Negative Integers

**Positive Integers** – The set of positive integers are expressed as

I^{+} or Z^{+ }= {1,2,3,4,5,6,7,8,9,10,11,12,13,………………}

I^{+} or Z^{+ }= {+1, +2, +3, +4, +5, +6, +7, +8, +9, +10, +11, +12, +13,………………}

**Negative Integers** – The set of positive integers are expressed as

I^{– }or Z^{– }= {–1, –2, –3, –4, –5, –6, –7, –8, –9, –10, –11, –12, –13,……}

** Note**:

*1. 0(Zero) is neither a Positive Integer nor a Negative Integer. It is neutral.*

*2. As stated above, the set of Natural Number can be expressed as*

*N = {1,2,3,4,5,6,7,8,9,10,11,12,13,……….}*

and

*The set of Positive Integer can be expressed as*

*I ^{+ }or z^{+}= [1,2,3,4,5,6,7,8,9,10,11,12,13,………………]*

*OR*

*I ^{+ }or z^{+}= [+1, +2, +3, +4, +5, +6, +7, +8, +9, +10, +11, +12, +13,………………]*

* *

*Hence we conclude that Natural Numbers are the set of Positive Integers.*

* *

*3. Except 0(***Zero)**, any number with or without + Sign (Positive) are always a +ve (Positive) Numbers

*For example : +3 and 3 carries same meaning i’e’, +3 =3*