   Another mathematical example, often given, of an impredicative definition is the definition of least upper bound of a bounded class of real numbers. If we identify a real with the set of rationals that are less than this real, we see that this least upper bound can be defined as the union of all elements in this class. Let us identify subsets of the rationals as predicates. For example, for rational numbers \(q, P(q)\) holds iff \(q\) is a member of the subset identified as \(P\). Now, we define the predicate \(L_C\) (a subset of the rationals) to be the least upper bound of class \(C\) as: