Write the rational number which is equal to its additive inverse

Last Updated : 03 Sep, 2021

A Number System is a way of Representing Numbers. Representation of Numbers is done by using digits or symbols. The Numbers that are represented by digits or symbols have the value and the value depends on the place, base, and value of the digits used. Let’s take a look at types of numbers in the number system,

Types of Numbers

In the number system, The biggest is the set of Complex numbers, it has both real numbers and Imaginary numbers, then comes real numbers and rational and irrational numbers are a part of real numbers only. There are Integers, whole numbers, and natural numbers that come under rational numbers. Let’s look at their definitions,

The Real Numbers

The Real Numbers are the Numbers that consist of All the numbers ie., all of the Rational Numbers and Irrational Numbers. Examples of real numbers are 3.33333, 4, 12/7, etc.

The Complex Numbers

The Complex Numbers are the numbers that are represented in (a+ib) form where b≠0, where a and b are Real Numbers and i is an imaginary unit with the value √-1. When the value is b. It is a Real Number since in (a+ib) b=0 then a+i*0 = a which is a real Number.

The Natural Numbers

The Natural Numbers are the Numbers that start from 1 and counts to Infinity. 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11….up to Infinity are Natural Numbers. It is a Subset of Whole Numbers.

The Whole Numbers

The Whole Numbers are the Natural Numbers with Including an extra number zero ie., the numbers that starts from 0 and counts to infinity are called Whole Numbers. It is a Superset of Natural Numbers. 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11,…up to Infinity.

The Integers

Integers set are the Number sets that consist of negative and positive numbers including zero. All the Basic Operations of Number System ie., Addition, Multiplication, Subtraction except Division will result in an Integer. Division may or may not result in Integer because when a smaller Numerator and Bigger Denominator are used in Division. It results in a fraction. That may be Rational Or Irrational

Irrational Number

A Number is called irrational if it cannot be expressed in the form of p/q, where p and q are Integers. In Other words, if it cannot be expressed as a Ratio of two Numbers. When a Number expressed in Decimal form, if it never terminates it is an Irrational Number. For example,

The Value π(PI) is 3.1415926…. the value never terminates, it is an Irrational Number.
√2 is 1.41421356237309… is irrational, hence the square roots of those numbers that are not perfect squares are irrational.
Square Roots of Perfect Squares are always Rational, for instance, √4 = 2, is a perfect square.

Rational Number

A Number is called Rational if it can be expressed in the form of p/q, where p and q are Integers. In other words, if it can be expressed as a Ratio of two Numbers. When a number is expressed in decimal form, if it terminates it is a Rational Number. Some Numbers that are never terminating but are recurring are rational numbers. For example, 0.0833333….. it is the decimal representation of 1/12 is a Rational Number. √4 is rational it can be expressed in p/q form i.e., 2/1