  In this paper we continue the investigation of a real number object, i.e., an
object representing the real numbers, in categories of relations. Our
axiomatization is based on a relation algebraic version of Tarski's axioms of
the real numbers. It was already shown that the addition of such an object
forms a dense, linear ordered abelian group. In the current paper we will focus
on the least-upper-bound property of such an object.
