[*][math]\LARGE \textcolor{blue}{\cal N}[/math] for [color=#0000ff]natural numbers[/color] {0, 1, 2, 3, ... }[br] [/*][*][math]\LARGE \textcolor{blue}{\cal Z}[/math] for [color=#0000ff]integers[/color] { ... , -2, -1, 0 , 1, 2, ... }[/*][*][math]\LARGE \textcolor{blue}{\cal R}[/math] for [color=#0000ff]real numbers[/color] which can be divided into two subgroups: [list][*][color=#0000ff]rational number ([/color][img]https://moodle.saimia.fi/amk/pluginfile.php/247256/mod_resource/content/1/eXe_LaTeX_math_11.gif[/img][color=#0000ff])[/color] can be expressed as fractions like [math]\Large 0.3=\frac{3}{10},\; \; 0.555... = \frac{5}{9}[/math]      [/*][/list][list][*][color=#0000ff]irrational numbers [/color]cannot be expressed as fractions like [math]\Large \pi, \sqrt 2[/math]   [/*][/list][/*][*] [math]\LARGE \textcolor{blue}{\cal C}[/math] for [color=#0000ff]complex numbers like [math]\Large2+3i[/math] [color=#000000](not part of this course)[/color] [/color][/*] [br][br]All  real numbers are [br][list][*][color=#0000ff]commutative[/color] [br][list][*][math]\Large a+b=b+a[/math][/*][*][math]\Large a \cdot b = b \cdot a[/math][/*][/list][/*] [br][*][color=#0000ff]assosiative[/color]  [br][list][*][math]\Large (a+b)+c=a+(b+c)=a+b+c[/math][/*][*][math]\Large (a\cdot b)\cdot c=a\cdot(b\cdot c)=a\cdot b\cdot c[/math][/*][/list][/*] [br][*][color=#0000ff]distributive[/color] [br][list][*][math]\Large a\cdot(b+c)=a\cdot b + a\cdot c[/math] [/*][/list][/*][br][/list]