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.

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, or purpose or fundamental rules they follow.

Following are the major types of numbers :

Natural 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

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

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.

Real Numbers

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.

Irrational Numbers

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

Imaginary Numbers

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.

Complex numbers

A Complex number is represented by the symbol “C.” The combination of real and imaginary numbers form 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 and b are real numbers while i is an imaginary number.

Hypercomplex Numbers

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

P-adic Numbers

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.

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

Number representations

Signed numbers

Types of Integer

Algebraic numbers

Non standard numbers

Computability and definability

Computable and Definable numbers are also one of its types.

Thus it can be said that a number is a mathematical value used to represent the quantity of an object. The 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 to types goes on adding with the passing years through many mathematicians.

FAQ (Frequently Asked Questions)

1. Which is the Only Even Prime Number?

Number 2 is the only even prime number.

2. State the Sub-Classifications of Number Representations.

Decimal, binary, hexadecimal, octal, duodecimal, sexagesimal, roman numerals, tally marks, fractions, continued fraction, scientific notation are the sub-classification of number representations.

3. What are the Signed Numbers?

Signed numbers are further classified as positive numbers, negative numbers, non-positive and non-negative numbers.

4. What are the Different Types of Integers?

Even and odd numbers, prime numbers, composite and polygonal numbers are the types of integers.

5. Classify Algebraic Numbers.

Algebraic numbers are classified as an algebraic number, transcendental trigonometric, quadratic surd, constructible number, and algebraic integer.

6. What are the Types of Non-Standard Numbers?

Transfinite, ordinal, cardinal, infinitesimals, hyperreal and surreal are the types of non-standard numbers.

7. How to find the Phase of a Complex Number?

All the operations of mathematics can be done on imaginary numbers the same as that of real numbers. A point in space on the complex plane represents a complex number in a rectangular form. While in Polar form a line whose length is the amplitude and by the phase angle denotes a complex number.

8. Is 0 Real or Imaginary Number?

Zero is considered an imaginary number since the imaginary number is the square root of a non-positive real number. When we look at zero, it is non-positive and also its own square root. Hence zero is termed as an imaginary number.

9. Is the Imaginary Number Positive or Negative?

An imaginary number is always a complex number. And a complex number is not greater than or less than zero. So imaginary numbers are neither positive nor negative.

10. What is the Number?

A string of digits used to indicate magnitude is known as a number. They also measure size, time, energy, distance, mass, etc.