In mathematics, a median algebra is a set with a ternary operation 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 (but not easy) to show that in the presence of the other three, axiom (3) is redundant. The fourth axiom implies associativity.
There are other possible axiom systems: for example the two
also suffice.
In a Boolean algebra, or more generally a distributive lattice, the median function satisfies these axioms, so that every Boolean algebra and every distributive lattice forms a median algebra.
Birkhoff and Kiss showed that a median algebra with elements 0 and 1 satisfying is a distributive lattice.
In mathematics, a medianalgebra is a set with a ternary operation ⟨ x , y , z ⟩ {\displaystyle \langle x,y,z\rangle } satisfying a set of axioms which...
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rules, reading comprehension, and mathematical skills such as arithmetic, algebra, and geometry. The Graduate Management Admission Council (GMAC) owns and...
dictionary. Medial may refer to: Medial magma, a mathematical identity in algebra Medial axis, in geometry the set of all points having more than one closest...
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