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The Categories, chap.7 /On Relatives/ contains a remarkable discussion in just a few pages and its author, supposedly Aristotle, might well be the first to have 'studied' asymmetric relations. So Aristotle distinguishes contrariety and reciprocation, adding further consideration on simultaneity. All relatives are 'reciprocated', but no all of them have '...


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William Rowan Hamilton's discovery of quaternions in the 19th century may be the first studied non-commutative relations. Here is Wikipedia: In mathematics, the quaternions are a number system that extends the complex numbers. They were first described by Irish mathematician William Rowan Hamilton in 1843 and applied to mechanics in three-dimensional ...


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