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In mathematics, a median algebra is a set with a ternary operation ⟨ x , y , z ⟩ {\displaystyle \langle x,y,z\rangle } satisfying a set of axioms which generalise the notions of medians of triples of real numbers and of the Boolean majority function.
The axioms are
The second and third axioms imply commutativity: it is possible to show that in the presence of the other three, axiom is redundant. The fourth axiom implies associativity.There are other possible axiom systems: for example the two
also suffice.
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