Number System

A number is a mathematical object used to count, measure and label. Numbers can be classified into sets called Number Systems.

Main Number System:

N	Natural	0, 1, 2, 3, 4, ... or 1, 2, 3, 4, ...
Z	Integer	..., −5, −4, −3, −2, −1, 0, 1, 2, 3, 4, 5, ...
Q	Rational	a/b where a and b are integers and b is not 0
R	Real	The limit of a convergent sequence of rational numbers
C	Complex	a + bi where a and b are real numbers and i is the square root of −1

Each of the number systems mentioned above is a proper subset of the next number system. Symbolically, N ⊂ Z ⊂ Q ⊂ R ⊂ C.

Summary:

Counting Numbers: Numbers to count.
Example: 1,2,3…… 

Zero: Number to express empty or nothing.
Example: 0

Whole Number: Counting number with zero.
Example: 0,1,2,3…..

Natural Number: Counting Number or Whole Number depending on subject

Negative Number: Numbers to count backwards.
Example: … -3,-2,-1

Integer: Negative Number with Whole Number.
Example: ..-3,-2,-1,0,1,2,3..

Even Number: Any integer that can be divided exactly by 2.
Example: ..-4,-2,0,2,4…

Odd Number: Any integer that cannot be divided exactly by 2.
Example: ..-3,-1,1,3…

Prime Number: An integer greater than 1 that has no positive divisors other than 1 and itself.
Example: 2, 3, 5, 7, 11, 13, 17…

Composite Number: An integer greater than 1 that is not a prime number.
Example: 4,6,8,9,10….

Fraction: Part of a whole.
Example: ½, ¼, ¾, 3/8…

Rational Number: Any number that can be written as a fraction. p/q : p and q are integers, q is not zero. Example: -4/3, 3/2, 2..

Irrational Number:  A number which cannot be expressed as a ratio of integers.
Example: √1, √2,√3, √5, π, e ..

Real Number: Rational and Irrational Numbers. x : x is a rational or an irrational number.
Example: 2, ¾, √1…

Imaginary Number: A number whose square is a negative Real Number.
Example: √-9 = 3i, -6i, 0.05i, πi..

Complex Number: Combination of a Real Number and an Imaginary Number.  a + bi, where a and b are real, and i is imaginary.
Example: 1+i, 0.5-3i,-2+ πi, √2+i/2.. 

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Related topics:
Numeral System   |   Number Types   |   Indian Numeral   |   Roman Numeral   |   Greek Numeral

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List of topics: Maths

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