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An intermediate value theorem for sequences with terms in a finite set

Mihai Caragiu·Laurence D. Robinson
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Abstract

We prove an intermediate value theorem of an arithmetical flavor, involving the consecutive averages of sequences with terms in a given finite set A. For every such set we completely characterize the numbers x ("intermediate values") with the property that the consecutive averages of every sequence with terms in A cannot increase from a value less than x to a value greater than x without taking the value x somewhere in between.

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Mihai Caragiu, Laurence D. Robinson. 2005-09-23. An intermediate value theorem for sequences with terms in a finite set. https://arxiv.org/abs/math/0509537

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