Types Of Numbers
Natural numbers : The counting numbers are known as natural numbers.
Ex : 1, 2, 3, 4, 5 ..............
Properties of Natural numbers:
i)The first and the smallest natural number is 1.
ii) Every natural number (except 1) can be obtained by adding 1 to the previous natural number i.e., the difference between any two consecutive natural numbers is 1.
iii) For the natural number 1, there is no previous natural numer.
iv) There is no last or greatest natural number.
V) We cannot c omplete the counting of all natural numbers. We express this fact by saying that there are infinitely many natural numbers.
Whole numbers : The natural numbers together with ‘0’ are known as whole numbers.
Ex : 0, 1, 2, 3 .......
Properties of Whole numbers:
i) The number zero is the first and the smallest whole number.
ii) There is no last or greastest whole number.
iii) There are infinitely many or uncountable numbers of whole numbers.
iv) All natural numbers are whole numbers.
v) All whole numbers are not natural numbers. For example , 0 is a whole number but it is not a natural number.
Even numbers : The numbers when divided by 2 give the remainder as ‘0’ are known as even numbers.
Ex : 2, 4, 6 .......
‘0’ is also an even number
Properties Of Even Numbers :
1. Numbers that can be expressed in the form of 2n, where ‘n’ is a whole number.
2. Numbers that can be divided into two equal parts.
3. When we divide an even number by 2, we get the remainder 0.
Examples: 2, 4, 18, 26,…
4. All numbers ending with 0, 2, 4, 6, 8 are referred to as even numbers
5. The sum of two even numbers is always even
6. The product of two even numbers is always even.
Odd numbers : The numbers when divided by 2 given the remainder as ‘1’ are known as odd numbers.
Ex : 1, 3, 5, .......
Sum of first ‘n’ odd natural numbers is
Sum of first ‘n’ even natural numbers is n (n+1)
Properties Of Odd Numbers :
1. Numbers that can be expressed in the form of 2n + 1, where ‘n’ is a whole number.
2. Numbers that cannot be divided into two equal parts.
3. When we divide an odd number by 2, we get the remainder 1.
Examples: 1, 5, 7, 9, 23,…
4. All numbers ending with 1, 3, 5, 7, 9 are referred to as odd numbers.
5. The sum of two odd numbers is always even
6. The product of two odd numbers is always odd
Successor & Predecessor:
The successor of a number is 1 more than the number and predecessor of a number is 1 less than then number.
Ex1. The successor of the number 6 is 6 + 1 = 7.
The predecessor of the number 6 is 6–1 = 5.
Ex2. The successor of the number 36 is 36+1 = 37
The predecessor of the number 6 is 36–1 = 35.
Ex3. The successor of the number -116 is -116+1 = -115
The predecessor of the number -116 is -116–1 = -117
The successor of a is a + 1.
The predecessor of a is a - 1.