Satz 2.1 Für alle $a,b,c,d\in IR$ gilt:

$\left(1\right)$ $-\left(-a\right)=a,-0=0,\left(-1\right)\cdot a=-a$.

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

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

$\left(4\right)$ $\frac{a}{b}=\frac{c}{d}\iff ad=bc$, falls $b,d\ne 0$.