ABSTRACT
This chapter deals with Dini’s derived numbers for continuous real-valued functions defined on various nondegenerate subintervals of the real line R. In terms of Dini’s derived numbers, a necessary and sufficient condition will be given for a continuous function to be constant on a subinterval of R. The chapter discusses in more detail Dini’s derived numbers with their application to some generalized version of the basic statement of Calculus. Since Dini’s derived numbers are defined in terms of limits of sequences, they look simpler (and, possibly, more convenient) than the usual concept of derivative which relies on the operation of taking limits along uncountable point sets. The chapter also includes exercise problems related to the concept of Dini’s derived numbers for continuous real-valued functions.
