From WikiChip
median algebra
Revision as of 14:46, 9 December 2015 by Jon (talk | contribs)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

Median algebra is an algebra with a single ternary operation satisfying a set of three axioms. This is largely a generalized concept of the majority function.

Axioms

For majority function Equation f colon double-struck upper B cubed right-arrow double-struck upper B with Equation w comma x comma y comma z element-of double-struck upper B :

Name Axiom
Majority Equation Maj left-parenthesis x comma x comma y right-parenthesis equals x
Commutative Equation Maj left-parenthesis x comma y comma z right-parenthesis equals Maj left-parenthesis x comma z comma y right-parenthesis equals Maj left-parenthesis y comma x comma z right-parenthesis equals Maj left-parenthesis y comma z comma x right-parenthesis equals Maj left-parenthesis z comma x comma y right-parenthesis equals Maj left-parenthesis z comma y comma x right-parenthesis
Associative Equation Maj left-parenthesis x comma w comma Maj left-parenthesis y comma w comma z right-parenthesis right-parenthesis equals Maj left-parenthesis Maj left-parenthesis x comma w comma y right-parenthesis comma w comma z right-parenthesis


Text document with shapes.svg This article is still a stub and needs your attention. You can help improve this article by editing this page and adding the missing information.
Retrieved from "https://en.wikichip.org/w/index.php?title=median_algebra&oldid=13005"