AN INTERMEDIATE VALUE THEOREM FOR SEQUENCES WITH TERMS IN A FINITE SET

Mihai Caragiu (U. S. A.) and Laurence D. Robinson (U. S. A.)

Abstract

We prove an intermediate value theorem of an arithmetical flavor involving the consecutive averages of sequences with terms in a given finite set For every such set we completely characterize the numbers Õ with the property that the consecutive averages of every sequence with terms in cannot increase from a value to a value without taking the value for some s with

Keywords and phrases: sequences, averages, intermediate values, time series.