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.
A directed set's preorder is called a direction. The notion defined above is sometimes called an upward directed set. A downward directed set is defined analogously, [2] meaning that every pair of elements is bounded below. [3] [a] Some authors (and this article) assume that a directed set is directed upward, unless otherwise stated. Other ...
Conversely, a strict partial order < on may be converted to a non-strict partial order by adjoining all relationships of that form; that is, := < is a non-strict partial order. Thus, if ≤ {\displaystyle \leq } is a non-strict partial order, then the corresponding strict partial order < is the irreflexive kernel given by a < b if a ≤ b and a ...
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 ...
This is a general situation in order theory: A given order can be inverted by just exchanging its direction, pictorially flipping the Hasse diagram top-down. This yields the so-called dual, inverse, or opposite order. Every order theoretic definition has its dual: it is the notion one obtains by applying the definition to the inverse order.
Prequalification and preapproval are two ways to help you determine how much of a mortgage you can afford. But they differ in timing, process and more. Take a closer look at what each step means ...
In many cases a market order will work fine for your needs, but you’ll also want to consider if you need to use a limit order, which offers some other benefits. A limit order works better when ...
In the branch of mathematics known as topology, the specialization (or canonical) preorder is a natural preorder on the set of the points of a topological space.For most spaces that are considered in practice, namely for all those that satisfy the T 0 separation axiom, this preorder is even a partial order (called the specialization order).