GetWiki

{{Short description|Mathematical ranking of a set}}{{distinguish|Weak order of permutations}}{{stack|{{Binary relations}}}}File:WeakOrder4Elements.png|thumb|A weak order on the set {a, b, c, d} where a is ranked below b and c, b and c are of equal rank, and d is ranked above b and c I) representation as a strict weak order ,===Strict weak orders are very closely related to total preorders or (non-strict) weak orders, and the same mathematical concepts that can be modeled with strict weak orderings can be modeled equally well with total preorders. A total preorder or weak order is a preorder in which any two elements are comparable.