Counting numbers are called natural numbers.
Thus 1,2,3,........ all are natural numbers
All Natural numbers and 0 forms the set of whole numbers
Thus 0,1,2,3,........ are the whole numbers.
clearly, every natural number is a whole number. O is whole number which is not a natural number.
All counting numbers, zero and negatives of counting numbers form the set of Integers
Thus ....-3,-2, -1, 0,1,2,3,........ are Integers.
A Natural number divisible by 2 is called an even number.
Thus 0,2,4,6,8,10,12,14,16........ are even numbers.
A counting number not divisible by 2 is called an odd number.
Thus 1,3,5,7,9,11........ are odd numbers.
A number other than 1 is called a prime number if it is divisible only by 1 and itself.
All prime numbers less than 100 are:-
2,3,5,7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67,71, 73, 79, 83, 89 and 97.
Total 25 prime numbers within 100.
Two natural numbers a and b are said to be co-prime if their HCF is 1.
For example:- (2,3), (4,5), (7,9), (8,11) etc. are pairs of co-primes.
A number, other than 1, which is not a prime number is called a composite numbers.
4,6,8,9,12,14..... etc. are composite numbers.
A series of numbers in which each is geater than that which precedes it by 1 is called consecutive numbers.
For Example:- 1,2,3,4,5,6,7,8 or 15,16,17,18 or 101,102,103 etc.
When the numbers are written in fractions, they are known as Rational Numbers. or, The numbers which can be written in the form p/q (where q ≠ 0) are called Rational numbers. They are denoted by Θ
For Example:- 1/2, 3/99, 45/47 etc.
The number which can not be written in the form of p/q are known as irrational number. (Where p and q are integers are q ≠ 0)
For Example:- √3 = 1.7321.... √2=1.4142.... but recurring decimals like 8/3=2.66666..... can be written in the p/q form so they are Rational Numbers.
Real Numbers include both Rational and Irrational numbers