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

**List of topics:**Maths

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