An Introduction
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 :
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 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.
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.
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:
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.
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.
FAQs on Types of Numbers
1. What are the properties of integers?
The properties of integers are as mentioned below:
They can be subtracted, added and multiplied.
For addition and multiplication of integers, commutative property is used.
The integers can be added and multiplied using associative property.
They can also be added and multiplied using the distributive property.
Zero is the additive identity of the integers.
One is the multiplicative identity of the integers.
2. What are the properties of rational and irrational numbers?
The properties of rational and irrational numbers are as follows:
Rational numbers can be added, subtracted, divided and multiplied. They follow the associative and commutative properties for multiplication and addition. They also follow the addition and subtraction by distributive property.
Irrational numbers can be added and multiplied using associative and commutative property. They are distributive under subtraction and addition.
3. What are whole numbers and what are their properties?
Whole numbers are all the natural numbers that start with zero. They consist of non-negative numbers and do not contain any fractions or decimals. They are represented by W. W has the numbers from zero to infinity. The whole numbers obey the associative and commutative property for multiplication and addition. The distributive property can also be used for them for multiplication and addition.
4. Which is the Only Even Prime Number?
Number 2 is the only even prime number.
5. 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.
6. What are the Signed Numbers?
Signed numbers are further classified as positive numbers, negative numbers, non-positive and non-negative numbers.
7. What are the Different Types of Integers?
Even and odd numbers, prime numbers, composite and polygonal numbers are the types of integers.
8. Classify Algebraic Numbers.
Algebraic numbers are classified as an algebraic number, transcendental trigonometric, quadratic surd, constructible number, and algebraic integer.
9. What are the Types of Non-Standard Numbers?
Transfinite, ordinal, cardinal, infinitesimals, hyperreal and surreal are the types of non-standard numbers.
10. 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.
11. 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 has its own square root. Hence zero is termed as an imaginary number.
12. 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.
13. 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.