The completeness axiom for the set $\Bbb R$ of real numbers states that
\correct any nonempty subset of $\Bbb R$ that is bounded above has a
supremum.
\wrong If $S$ is a bounded subset of $\Bbb R$ then the supremum of~$S$
is the maximal element of~$S$.
\wrong If $S\subset\Bbb R$ is bounded below then $S$ has a supremum.
\wrong If $S\subset\Bbb R$ is unbounded then $S$ has no supremum.
\wrong If a set $S\subset \Bbb R$ has no supremum, then $S$ is empty.
