The Archimedean Property for the real numbers $\Bbb R$ states that
\correct If  $a>0$ and $b>0$,
then there exists some positive integer $n$ such that $na>b$.
\wrong If $a>0$ and $b>0$ then $ab>0$.
\wrong If $a>0$ then there exists a positive integer $n$ such that
$\frac1a>n$.
\wrong the completeness axiom fails for the set $\Bbb Z$ of integers.
\wrong If $a>0$ and $b>0$ then there exists a positive integer $n$
such that $a^n>b$.
