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Monochromatic and monotonic: A theorem of Ramsey and an application to analysis

Published online by Cambridge University Press:  01 August 2016

Keith Austin*
Affiliation:
Department of Pure Mathematics, The University, Sheffield S3 7RH

Extract

A familiar result is that in any group of six people there are three who either all know each other or are all strangers to each other. This can be reformulated to say that, if six points are marked on a piece of paper and every pair of points is joined by a red or blue line, then there will be a monochromatic triangle, i.e. one which is all red or all blue. This result is related to a theorem which the Cambridge philosopher Frank Ramsey proved in 1930.

Type
Research Article
Copyright
Copyright © The Mathematical Association 1988

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