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

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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.
13 pages

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General Mathematics, 11B99; 26D15

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http://salesiana.dossiersoluciones.com/handle/123456789/94866

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0509537
 http://arxiv.org/abs/math/0509537

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arXiv