${\displaystyle {}a\geq b\,}$

genau dann, wenn

${\displaystyle {}a+c\geq b+c\,}$

ist.

${\displaystyle {}a\geq b\,}$

und

${\displaystyle {}c\geq d\,}$

folgt

${\displaystyle {}a+c\geq b+d\,.}$

${\displaystyle {}a\geq b\,}$

folgt

${\displaystyle {}ca\geq cb\,.}$

${\displaystyle {}a\geq b\,}$

und

${\displaystyle {}c\geq d\,}$

folgt

${\displaystyle {}ac\geq bd\,.}$

${\displaystyle {}c\geq 1\,}$

und

${\displaystyle {}ca\geq cb\,.}$

folgt

${\displaystyle {}a\geq b\,.}$