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m →Distributive lattices and median algebras: merge <math> |
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satisfies certain key axioms, which it shares with the usual [[median]] of numbers in the range from 0 to 1 and with [[median algebra]]s more generally:
*[[Idempotence]]: {{tmath|1=m(a,a,b) = a}} for all ''a'' and ''b''.
*[[Commutativity]]:
*[[Distributivity]]: {{tmath|1=m(a,m(b,c,d),e) = m(m(a,b,e),c,m(a,d,e))}} for all ''a'', ''b'', ''c'', ''d'', and ''e''.
*[[Identity element]]s: ''m''(0,''a'',1) = ''a'' for all ''a''.
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