This is my first post on this blog. This post is about one of the first mathematical definitions I ever made in my life, which I call circular relations. A circular relation is a binary relation on a set , such that the following property holds:
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Note the contrast with transitivity, where instead of in the consequent, we have . An example of a relation having this property is the “defeats” relation in the game of Rock-Paper-Scissors: Rock defeats Scissors, Scissors defeats Paper, but Paper defeats Rock. My next post will be about proving a theorem about circular relations, namely that a binary relation is an equivalence relation if and only if is both a reflexive and circular relation.