Satz 2.1 Für alle $a,b,c,d\in I\phantom{\rule{-1.705pt}{0ex}}R$ gilt:

$\left(1\right)$ $-\left(-a\right)=a,\phantom{\rule{3.61665pt}{0ex}}\phantom{\rule{3.61665pt}{0ex}}-0=0,\phantom{\rule{3.61665pt}{0ex}}\phantom{\rule{3.61665pt}{0ex}}\left(-1\right)\cdot a=-a$.

$\left(2\right)$ $\frac{a}{1}=a.$

$\left(3\right)$ $\frac{1}{\frac{1}{a}}=a$, falls $a\ne 0$.

$\left(4\right)$ $\frac{a}{b}=\frac{c}{d}\phantom{\rule{3.61665pt}{0ex}}⇔\phantom{\rule{3.61665pt}{0ex}}ad=bc$, falls $b,\phantom{\rule{0em}{0ex}}d\ne 0$.