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Chaotic Orderings of the Rationals and Reals

Hayri Ardal, Tom Brown and Veselin Jungić
The American Mathematical Monthly
Vol. 118, No. 10 (December 2011), pp. 921-925
DOI: 10.4169/amer.math.monthly.118.10.921
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Page Count: 5
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Chaotic Orderings of the Rationals and Reals
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Abstract In this note we prove that there is a linear ordering of the set of real numbers for which there is no monotonic 3-term arithmetic progression. This answers the question (asked by Erdős and Graham) of whether or not every linear ordering of the reals must have a monotonic k-term arithmetic progression for every k.

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