Number Systems – 7 – Do you know them?
September 8, 2026 · 4 min read · 35 views · BSRB - Quantitative Aptitude & Reasoning
The knowledge of the Number System is essential for understanding the Arithmetics of Numbers. Before applying any operations on any numbers it is pertinent to know about the numbers to which system they belong to. The largest number system is Complex Number system followed by Real Number system. A brief of evolution of the number systems is discussed here.
Types of Numbers
The Natural numbers in use since long long ago are 1,2,3,…. . These are called natural Numbers of counting under use for all practical purposes. These are also called as Positive integers.
When zero is added to natural numbers, then the number system consisting f numbers such 0,1,2,3 …. Is called as the system of Whole numbers.
When negative numbers such as -1,-2,-3,… are added to the whole numbers then the system is called as the system of integers. The Negative part of integers is called as the negative integers. Thus ………-3,-2,-1,0,1,2,3……… is a system of integer numbers.
When an integer is divided by another integer it results in a rational number. Thus from the system of integers the system of rational numbers is developed. Note that all integers are part of rational numbers. For Example , \frac{3}{1} is also a rational number and also as \frac{3}{7} .
Hence all integers are also rational numbers. Some rational numbers do get themselves terminated at one particular level during division operation. Some rational numbers which are non terminable for any length of chain are also available.. The example for the rational numbers is \frac{3}{7}=0.428571.... is of non-terminable type.
Some type of numbers which do not belong to any above type of numbers and also cannot be represented as rational numbers are irrational numbers. Some examples of irrational numbers are \sqrt{2} = 1.414213… and \log3=0.477... These can not be represented as ratio of two integer numbers.
Hierarchy of System of Numbers
When above all systems of numbers are put together in a system that system of numbers is called as the system of Real Numbers. The Hierarchy of System of Numbers thus can be shown in the order of ascendent is,
- Natural Numbers – All Positive integers
- Whole Numbers = Natural Numbers + Zero
- Integers = Whole Numbers + Negative integers
- Rational Numbers = Ratios of all Integers ( Full system of integers included )
- Irrational numbers = The Numbers which can not be expressed as Rational Numbers.
- REAL NUMBERS = RATIONAL NUMBERS + IRRATIONAL NUMBERS
Complex Number System
If we have to find out the square root a negative number we do not have any number in Real number system. For example there is no real number equivalent of \sqrt{-1} . Hence there felt a necessity of inventing another system in addition to Real Number system. Even though most of our day to day life the Real Number System is Sufficient to take care of of our needs. But for advanced scientific studies, in addition to Real system the system addressing the meaning of \sqrt{-1} ( Complex Number ) is also required.
As necessity is the father of invention, a system called COMLEX NUMBER SYSTEM is invented and added to the Real Numbers. hence Complex Number System is the largest number system. The Real Numbers are defined inside the Complex Number System. Hence the latest hierarchy is ,
- Natural Numbers – All Positive integers
- Whole Numbers = Natural Numbers + Zero
- Integers = Whole Numbers + Negative integers
- Rational Numbers = Ratios of all Integers ( Full system of integers included )
- Irrational numbers = The Numbers which can not be expressed as Rational Numbers.
- Real Numbers = Rational Numbers + Irrational Numbers
- COMPLEX NUMBER SYSTEM = COMPLEX NUMBERS ( INCLUDING REAL NUMBERS )
Largest System
The largest system is the Complex Number System as above. The above knowledge of the Number System is essential for proper operations to be performed on the numbers. The Arithmetic is the process of operations that are performed on the numbers.
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