Derived Sets

A derived set is a set resulting from one or more set operations on fundamental or derived sets which does not simplify to a fundamental set, e.g. (union (set 1 2 3) string) (the union of $\{ 1 2 3 \}$ and the set of strings) or (difference real integer) (the open set resulting from $\Re - I$). Note that (union (differencereal integer) integer) simplifies to real and hence is a fundamental, not a derived set^1.4