[Maths Class Notes] on Types of Numbers Pdf for Exam

The ten symbols or digits or numbers as they are called play an important role in our day-to-day life. These simple ten digits create an infinite array of numbers on which the whole universe is dependent. Age, height, weight, dimension, time, dates, PINs, bank accounts, telephone numbers, station numbers, and on and on, nothing could have been expressed without the evolution of numbers. Engineers, accountants, cashiers, manufacturers, carpenters, scientists or laymen, anyone and everyone, need different types of numbers to express themselves.

Overview on Types of Numbers 

Numbers can be defined as those digits which represent the quantity of something. The magnitude of the number used is used to define the quantity’s size which can be either small or large. They can exist in different types like decimals, fractions, or other forms. They are broadly classified as discrete or continuous. The countable numbers are the discrete numbers and the ones that can’t be counted are named continuous numbers. The discrete numbers are natural numbers, rational numbers, and whole numbers as they are countable. The continuous numbers are real numbers that are of large magnitude and cannot be counted. There exists a large number of numbers between the real numbers and they cannot be counted.

Numbers can be further classified into sets and each number is a subset of other numbers. For example, all the natural numbers are the subset of whole numbers. Similarly, the whole numbers are a subset of integers. The rational numbers set has all the integers and fractions and the rational numbers and irrational numbers set form the real numbers. This is how the numbers form a set. 

Types of Numbers

A wide variety of infinite arrays, patterns, or numbers have been derived from the basic ten digits. These numbers are classified into different types of numbers according to their properties, purpose, or fundamental rules they follow.

Following are the major types of numbers :

The symbol of natural numbers is “N.” In common terms, the digits that are used for counting or ordering are known as Natural numbers. Mathematically a convenient set of codes used for counting or ordering is known as natural numbers. Natural numbers are also known as counting numbers. 

Natural numbers start from zero to infinity. However, when it includes “0” also then it is called whole numbers.

Integers are denoted by “Z” or “Z+.” The word has its origin in the Latin word integer, which means whole. A number that is written without a fractional component is known as Integers. It contains positive as well as negative numbers.

Rational numbers are represented by the symbol “Q.” When a ratio of an integer to a non-zero integer is expressed in numbers, it is known as rational numbers. All the integers are rational numbers, however not all rational numbers can be termed as integers.

A set of real numbers is denoted by “R.” When a number or value of a continuous quantity can constitute a distance on a number line, such numbers are known as Real numbers. A real number includes all the rational numbers, integers, irrational numbers. Real numbers can also be used to measure time, energy, mass, velocity, etc.

A real number that cannot be written in a fraction is called an irrational number.

When a product of real numbers with that of the square root of -1 is taken, the resultant number is known as an imaginary number. An example of both real and imaginary numbers is the number “0”. One can also say that when a complex number is written as a real number multiplied by the imaginary unit I it is known as an imaginary number. The only property that defines an imaginary number is i2 = −1.

A Complex number is represented by the symbol “C.” The combination of real and imaginary numbers forms a complex number. It also includes the sum and differences between real and imaginary numbers.

The equation that represents a complex number is a+bi

Here a and b are real numbers while i is an imaginary number.

Various number system extensions are categorized under hypercomplex numbers. These include quaternions, octonions, sedenions, tessarines, coquaternions, and biquaternions.

These are the number of systems that are constructed considering the limits of rational numbers but are different from the one that is used to construct the real numbers.

Other Types of Numbers

The types of numbers are also classified considering other parameters too. The other types of numbers are classified and sub-classified as follows:

Computable and Definable numbers are also one of its types.

Conclusion

Thus it can be said that a number is a Mathematical value used to represent the quantity of an object. Numbers have such an integral part in our life that one cannot imagine surviving without them. Numbers are important in both classical and recreational Mathematics. Different types of numbers form unique patterns which are used for solving mathematical problems. These patterns will have basic ten numbers along with specific relationships and or equations. This world of types of numbers is vast and deep, and the classification of types goes on adding with the passing years through many Mathematicians.