Order theory is a branch of mathematics that investigates the intuitive notion of order using binary relations. It provides a formal framework for describing statements such as "this is less than that" or "this precedes that". This article introduces the field and provides basic definitions. A list of order-theoretic terms can be found in the ...

Examples In horse racing, the use of photo finishes has eliminated some, but not all, ties or (as they are called in this context) dead heats, so the outcome of a horse race may be modeled by a weak ordering. In an example from the Maryland Hunt Cup steeplechase in 2007, The Bruce was the clear winner, but two horses Bug River and Lear Charm tied for second place, with the …

Please help to improve this article by introducing more precise citations. (February 2016) ( Learn how and when to remove this template message) In mathematics, a total or linear order is a partial order in which any two elements are comparable. That is, a total order is a binary relation. ≤ {\displaystyle \leq } on some set. X {\displaystyle X}