Some undecidable problems involving elementary functions of a real variable

Abstract

Let E be a set of expressions representing real, single valued, partially defined functions of one real variable. E * will be the set of functions represented by expressions in E . If A is an expression in E , A(x) is the function denoted by A . It is assumed that E* contains the identity function and the rational numbers as constant functions and that E* is closed under addition, subtraction, multiplication and composition.