Natural Numbers
Natural numbers are counting numbers. They are denoted by N. For example N = {1,2,3,4,...}
- All natural numbers are positive.
- Zero is not a natural number. Therefore, 1 is the smallest natural number.
Whole Numbers
All natural numbers and zero form the set of whole numbers. Whole numbers are denoted by W. For example W = {0,1,2,3,...}
- Zero is the smallest whole number.
Whole numbers are also called as non-negative integers.
Integers
Whole numbers and negative numbers form the set of integers. They are denoted by I
For example I = {...,-4,-3,-2,-1,0,1,2,3,4,...}
Even Numbers
Acounting number which is divisible by 2, is called an even number. For example 2, 4, 6, 8, 10, 12, ....
Odd Numbers
A counting number which is not divisible by 2, is known as an odd number.
Prime Numbers
A counting number is called a prime number when it is exactly divisible by, 1 and itself. For example 2, 3, 5, 7, 11, 13, ...
- 2 is the only even number which is prime.
- A prime number is always greater than 1.
- 1 is not a prime number. Therefore, the lowest odd prime number is 3.
- Every prime number greater than 3 can be represented by 6n + 1, where n is integer.
Composite Numbers
Composite numbers are non-prime natural numbers. They must have atleast one factor apart from 1 and itself.
For example 4, 6, 8, 9, etc.
- Composite numbers can be both odd and even.
- 1 is neither a prime number nor composite number.
Coprimes
Two natural numbers are said to be coprimes, if their HCF is 1. For example (7, 9), (15, 16)
- Coprime numbers may or may not be prime.
Rational Numbers
A number that can be expressed as p/q is called a rational number, where p and q are integers and p<q
Examples 7/9, 8/9 etc
Irrational Numbers
The numbers that cannot be expressed in the form of p/q are called irrational numbers, where p and q are integers
Examples root(2), pai,.. etc
Real Numbers
Real numbers include rational and irrational numbers both
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