Introduction
Types of numbers
What is a Number Line?
A visual representation of numbers on a straight line drawn either horizontally or vertically is known as a number line. There are three parts of a number line which are – negative side, zero, and positive side. Numbers to the left of 0 are negative numbers and numbers to the right of 0 are all positive numbers.
What Is an Integer?
An integer is a number with no decimal or fractional part, from the set of negative and positive numbers, including zero. Examples of integers are: -5, 0, 1, 5, 8, 97.
A set of integers, which is represented as Z, includes:
Positive Integers: An integer is positive if it is greater than zero. Example: 1, 2, 3 . . .
Negative Integers: An integer is negative if it is less than zero. Example: -1, -2, -3 . . .
Zero is defined as neither negative nor positive integer. It is a whole number.
Z = {… -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, …}
What Is Natural numbers ?
Natural number is a part of the number system, including all the positive integers from 1 to infinity. They are a part of real numbers including only the positive integers, but not zero, fractions, decimals, and negative numbers.
The set of natural numbers include only the positive integers, i.e., 1, 2, 3, 4, 5, 6, ……….∞.
What are Whole Numbers?
Whole Numbers are the set of natural numbers along with the number 0. The set of whole numbers in Mathematics is the set {0, 1,2,3,…}.This set of whole numbers is denoted by the symbol W.
W = {0,1,2,3,4…}
Here are some facts about whole numbers, which
All natural numbers are whole numbers.
All counting numbers are whole numbers.
All positive integers including zero are whole numbers.
What Are Prime Numbers?
A number greater than 1 with exactly two factors, i.e. 1 and the number itself is defined as a prime number. In other words, if a number cannot be divided into equal groups, then it is a prime number. Eg. 2,3,5,7,11….
What are Co-prime Numbers?
If the only common factor of two numbers a and b is 1, then a and b are co-prime numbers. In this case, (a, b) is said to be a co-prime pair. Co-prime numbers are also referred to as relatively prime or mutually prime numbers.
Eg. (2,3), (5,7)…..
What Are Even Numbers ?
An even number is a number that is a multiple of 2.
Eg . 2,4,6,8,……….
What are Odd Numbers ?
Odd numbers definition is given as those numbers which cannot be divided into two parts equally.
Odd numbers are basically integer numbers that cannot be categorized into groups of two each. For example: 1, 3, 5, 7, etc.
What are Real Numbers?
Any number that we can think of, except complex numbers, is a real number. Real numbers include rational numbers like positive and negative integers, fractions, and irrational numbers.
The set of real numbers, which is denoted by R, is the union of the set of rational
Observe the following table to understand this better. The table shows the sets of numbers that come under real numbers.
What are Rational Numbers?
A rational number is a number that is of the form p/q where p and q are integers and q is not equal to 0. The set of rational numbers is denoted by Q. In other words, If a number can be expressed as a fraction where both the numerator and the denominator are integers, the number is a rational number.
Some examples 1/2 , 4/3…….
What are Irrational Numbers?
Irrational numbers are the set of real numbers that cannot be expressed in the form of a fraction, p/q where p and q are integers. The denominator q is not equal to zero (q ≠ 0).
Common Examples of Irrational Numbers
ㄫ(pi) is an irrational number. π=3⋅14159265…. Since the value of ㄫ is closer to the fraction 22/7, we take the value of pi as 22/7 or 3.14 (Note: 22/7 is a rational number.)
√2 is an irrational number.
What are Decimals?
There are three types of Decimals
Terminating 3.25, 1.24 …..etc.
Non-Terminating but Repeating 1.333333…., 1.121212….,
Non-Terminating Non Repeating(Irrational):
π = 3.1415926535….,
e = 2.718281828……,
√2 = 1.4142135…..
What are Complex Numbers?
A complex number is the sum of a real number and an imaginary number. A complex number is of the form a + ib and is usually represented by z. Here both a and b are real numbers. The value ‘a’ is called the real part which is denoted by Re(z), and ‘b’ is called the imaginary part Im(z). Also, ib is called an imaginary number.
Some of the examples of complex numbers are ..
2+3𝑖 , 5-7𝑖,1+2/3 𝑖….
