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INTRODUCTION OF INTEGERS

__INTRODUCTION OF INTEGERS__

**When a smaller whole
number is subtracted from a larger whole number, then we always get a whole
numbers. Thus 55 – 25 = 30, which is a whole number.**

**
And 65
– 45 = 20, which is a whole number.**

**
But, 15 – 35 = ? **

**It has been observed that, when a bigger whole number is subtracted from a smaller whole number then
we do not get the whole number.**

**Thus the set of all
whole numbers is inadequate for subtraction. So, we need a new type of number
which may represent these above types of difference. **

**Thus corresponding to
natural numbers 1, 2, 3, 4, 5, 6, 7, 8,……………….. etc. , we would like to
introduce a new numbers denoted by -1 ( minus one) , -2 (minus two) , -3 (minus
three), -4 (minus four), -5 (minus five), -6 (minus six), -7 (minus seven), -8
(minus eight). If we write the numbers with the minus sign then the numbers are
looks like as follows –**

**-1, -2, -3, -4, -5,
-6, -7, -8, -9, -10,………………..**

**-1 and +1
or 1 are called the opposite of each other, **

**-4 and +4
or 4 are called the opposite of each other, **

**Thus we get a new set
of numbers of Integers, and Integer is denoted by ‘I’**

**The numbers 1, 2, 3,
4, 5, 6, 7, 8, 9, 10,………….. are known as (+) positive Integers.**

**And the numbers -1, -2,
-3, -4, -5, -6, -7, -8, -9, -10,……………. Are known as (-) negative Integers.**

**0 (Zero) is such a
type of Integer which is neither (+) positive nor (-) negative**

**Thus we can get new
set of Integers which are given below-**

**I = ( ……………….. -8,
-7, -6, -5, -4, -3, -2, -1, 0 , 1, 2 , 3, 4, 5, 6, 7, 8,………………. )**

**We may denote
positive Integers like that- ………………, +11 , +12, +13, +14, +15, +16, +17,
+18, +19, +20,…….. instead of ………………….., 11, 12, 13, 14, 15, 16, 17, 18, 19,
20,……………………**