Ad
related to: partial order vs pre order on amazon fire stick remote download
Search results
Results From The WOW.Com Content Network
Both of these are special cases of a preorder: an antisymmetric preorder is a partial order, and a symmetric preorder is an equivalence relation. Moreover, a preorder on a set X {\displaystyle X} can equivalently be defined as an equivalence relation on X {\displaystyle X} , together with a partial order on the set of equivalence class.
Preorder (Quasiorder) Partial order Total preorder Total order Prewellordering Well-quasi-ordering Well-ordering Lattice Join-semilattice Meet-semilattice Strict partial order Strict weak order Strict total order Symmetric: Antisymmetric: Connected: Well-founded: Has joins: Has meets: Reflexive: Irreflexive: Asymmetric
However the product order of two total orders is not in general total; for example, the pairs (,) and (,) are incomparable in the product order of the ordering < with itself. The lexicographic combination of two total orders is a linear extension of their product order, and thus the product order is a subrelation of the lexicographic order.
A total order is a total preorder which is antisymmetric, in other words, which is also a partial order. Total preorders are sometimes also called preference relations . The complement of a strict weak order is a total preorder, and vice versa, but it seems more natural to relate strict weak orders and total preorders in a way that preserves ...
Given a set and a partial order relation, typically the non-strict partial order , we may uniquely extend our notation to define four partial order relations , <,, and >, where is a non-strict partial order relation on , < is the associated strict partial order relation on (the irreflexive kernel of ), is the dual of , and > is the dual of <.
Get AOL Mail for FREE! Manage your email like never before with travel, photo & document views. Personalize your inbox with themes & tabs. You've Got Mail!
A market order instructs your broker to execute your trade of a security at the best available price at the moment you send in your order. If you’re buying, you’ll transact at the seller’s ...
For example, by definition, a prefilter or filter base is a non-empty family of sets that is a directed set with respect to the partial order and that also does not contain the empty set (this condition prevents triviality because otherwise, the empty set would then be a greatest element with respect to ).