Question

How do you classify real numbers?

Answer 1

Hint: Here in this question, we have to classify the real numbers means we have to discuss the topic of what is real numbers or definition of real number, what are all the different types of numbers including in it or set of real numbers and Examples of real numbers are explained in the below section.

Complete step-by-step answer:
Real numbers are simply the combination of rational and irrational numbers, in the number system. In general, all the arithmetic operations can be performed on these numbers and they can be represented in the number line, also. At the same time, the imaginary numbers are the un-real numbers, which cannot be expressed in the number line and is commonly used to represent a complex number.
Definition of Real number
Real numbers can be defined as the union of both the rational and irrational numbers. They can be both positive or negative and are denoted by the symbol “R”. All the natural numbers, decimals and fractions come under this category
Set of real number with examples
Natural numbers - Contain all counting numbers which start from 1.
Example: All numbers such as 1, 2, 3, 4, 5, 6,…
Whole Numbers - Collection of zero and natural number.
Example: All numbers including 0 such as 0, 1, 2, 3, 4, 5, 6,…
Integers- The collective result of whole numbers and negative of all natural numbers.
Example: \[ - \infty , \cdot \cdot \cdot 0,1,2,3, \cdot \cdot \cdot + \infty \]
Rational Numbers- Numbers that can be written in the form of \[\dfrac{p}{q}\] where \[q \ne 0\]
Example: 3, -7, -100, \[\dfrac{1}{2}\], \[\dfrac{5}{3}\], 0.16, 0.4666 etc
Irrational Numbers- All the numbers which are not rational and cannot be written in the form of \[\dfrac{p}{q}\]
Example: \[\sqrt 2 \], \[\pi \], \[\sqrt 3 \], \[2\sqrt 2 \] and \[ - \sqrt {45} \] etc
These are all the numbers which include in the set of real numbers or the union of all these numbers are known as Real numbers.

Note: Some questions in mathematics are explained in a detailed way. Here the question is about the real numbers. We should know about the different kinds of numbers that are classified in mathematics and how they are different from each other. Better to explain with example