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,……………………