# Number Sets

Keywords: number sets, natural numbers, integers, rational numbers, irrational numbers, real numbers, complex numbers, relation between number sets

## Natural Numbers

$\mathrm{ℕ}=\left\{0,1,2,3,4,5,6···\right\}$

## Integers

$\mathrm{ℤ}=\left\{···,-3,-2,-1,0,1,2,3,···\right\}$

## Rational Numbers

A rational number is any number that can be expressed as fraction of two integers.

## Irrational Numbers

${\mathrm{ℚ}}^{*}=\left\{···,-\sqrt{3},\sqrt{2},\mathrm{\pi },\mathrm{e},···\right\}$

Irrational number is any number that cannot be expressed as a ratio between two integers.

## Real Numbers

$\mathrm{ℝ}=\mathrm{ℚ}\cup {\mathrm{ℚ}}^{*}$

All Rational and Irrational numbers.

## Relation Between Number Sets

$\mathrm{ℕ}\subset \mathrm{ℤ}\subset \mathrm{ℚ}\subset \mathrm{ℝ}\subset \mathrm{ℂ}$