Hello Aspirants!
In this post, we will deal with various types of numbers in the number system.
Under this section " Number System: Various Types of Numbers " we will deal with the following :
- Natural Numbers
- Whole Numbers
- Integers
- Prime Numbers
- Composite Numbers
- Even Numbers
- Odd Numbers
- Rational Numbers
- Irrational Numbers
- Real Numbers
Natural Numbers: All numbers which are used for counting is called Natural Number. As the counting starts from 1, so all numbers including 1 and above are called a natural number. For example : 1, 2, 3, 4, 5, .......
Note: Natural Numbers are also known as Counting Numbers.
Natural Numbers are represented as " N " where N = { 1, 2, 3, 4, 5, .... }
}
Smallest Natural Number is 1 and Largest Natural Number is
0 ( zero ) is not a natural number
Whole Numbers: All natural numbers including 0 ( zero ) is known as the whole number. As the whole number starts from 0 ( zero ), so all numbers including 0 ( zero ) and above are called a whole number. For example : 0, 1, 2, 3, 4, .......
Whole Numbers are represented by " W " where W = { 0, 1, 2, 3, 4, 5, ..... }
Smallest Whole Number is 0 and the Largest Whole Number is
Integers: All natural numbers and their negatives and 0 ( zero ) is called integers. For example : -2, -1, 0, 1, 2, .....
Integers are represented by " Z " where Z = { -, ..... -3, -2, -1, 0, 1, 2, 3, ..... }
The largest integer is and the Smallest integer is -
Prime Numbers: Positive Whole Numbers which are greater than 1 and have only two factors namely 1 and the number itself are called prime numbers. For example : 2, 3, 5, 7, 11, ......
Composite Numbers: Positive Whole Numbers which are greater than 1 and have more than two factors are called Composite Numbers. For example : 4, 6, 8, 9, 10, ......
Even Numbers: All integers which are exactly divisible by 2 i.e. if the required integers are divided by 2, it yields 0 ( zero ) as the remainder, then the required integers are called even numbers. For example : ..... -4, -2, 2, 4, ......
Odd Numbers: All integers which are not exactly divisible by 2 i.e. if the required integers are divided by 2, it yields a non-zero number as the remainder, then the required integers are called odd numbers. For example : .... -5, -3, 3, 5, .....
Rational Numbers: A number in the form of fraction p/q where q is not equal to zero is called a rational number. For example 2/5, 1/2, 1/3...
Every integer is a rational number. For example, -2 can be expressed as -2/1 and thus it is a rational number
Irrational Numbers: A number that cannot be written in the form of a fraction P/q where q is not equal to zero is called an irrational number. For example √2, √3 .....
All non-terminating, non-repeating decimals are irrational numbers.
The square root of any prime number is an irrational number
Real Numbers: A number which is either from a set of rational numbers or from irrational numbers are called real numbers.
In other words, Real Numbers are numbers that can be represented in decimal that have a finite or infinite sequence of digits to the right of the decimal point. A real number can be positive, negative, or zero.
Integers are represented by " Z " where Z = { -, ..... -3, -2, -1, 0, 1, 2, 3, ..... }
The largest integer is and the Smallest integer is -
Prime Numbers: Positive Whole Numbers which are greater than 1 and have only two factors namely 1 and the number itself are called prime numbers. For example : 2, 3, 5, 7, 11, ......
Composite Numbers: Positive Whole Numbers which are greater than 1 and have more than two factors are called Composite Numbers. For example : 4, 6, 8, 9, 10, ......
Even Numbers: All integers which are exactly divisible by 2 i.e. if the required integers are divided by 2, it yields 0 ( zero ) as the remainder, then the required integers are called even numbers. For example : ..... -4, -2, 2, 4, ......
Odd Numbers: All integers which are not exactly divisible by 2 i.e. if the required integers are divided by 2, it yields a non-zero number as the remainder, then the required integers are called odd numbers. For example : .... -5, -3, 3, 5, .....
Rational Numbers: A number in the form of fraction p/q where q is not equal to zero is called a rational number. For example 2/5, 1/2, 1/3...
Every integer is a rational number. For example, -2 can be expressed as -2/1 and thus it is a rational number
Irrational Numbers: A number that cannot be written in the form of a fraction P/q where q is not equal to zero is called an irrational number. For example √2, √3 .....
All non-terminating, non-repeating decimals are irrational numbers.
The square root of any prime number is an irrational number
Real Numbers: A number which is either from a set of rational numbers or from irrational numbers are called real numbers.
In other words, Real Numbers are numbers that can be represented in decimal that have a finite or infinite sequence of digits to the right of the decimal point. A real number can be positive, negative, or zero.
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