Properties of Natural Numbers
The properties of natural numbers are as follow:
(i) Natural numbers are also called counting numbers.
(ii) The first and the smallest natural number is 1 (one).
(iii) Every natural number (except 1) can be obtained by adding 1 to the previous natural number.
(iv) For the natural number 1, there is no ‘previous’ natural number (Though 1 = 0 + 1, but 0 is not a natural number).
(v) There is no last or greatest natural number since they are infinite.
(vi) Natural numbers are denoted by 'ℕ' normally.
(vii) We cannot complete the counting of all natural numbers. We express this fact by saying that there are infinitely many natural numbers.
Note:
The
counting numbers 1, 2, 3, 4, ..... are called naturals numbers. The set
of natural numbers is denoted by 'ℕ'. Thus, ℕ = {1, 2, 3, 4, .....}.
Even Natural Numbers (E):
A
system of naturals numbers, which are divisible by 2 or are multiples
of 2, is called a set of even numbers. It is denoted by 'E'.
Thus, E = {2, 4, 6, 8, 10, 12, .....}
There are infinite even numbers.
Odd Natural Numbers (O):
A
system of naturals numbers, which are not divisible by 2 or are not
multiples of 2, is called a set of odd numbers. It is denoted by 'O'.
Thus, O = {1, 3, 5, 7, 9, 11, .....}
There are infinite odd numbers.
Taking together the odd and even numbers, we get Natural Numbers.
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