In mathematics, the order of a finite group is the number of its elements. If a group is not finite, one says that its order is infinite.The order of an element of a group (also called period length or period) is the order of the subgroup generated by the element.If the group operation is denoted as a multiplication, the order of an element a of a group, is thus the smallest positive integer m ...

First-order logic—also known as predicate logic, quantificational logic, and first-order predicate calculus—is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science.First-order logic uses quantified variables over non-logical objects, and allows the use of sentences that contain variables, so that rather than propositions such as "Socrates …

A lattice is an abstract structure studied in the mathematical subdisciplines of order theory and abstract algebra.It consists of a partially ordered set in which every pair of elements has a unique supremum (also called a least upper bound or join) and a unique infimum (also called a greatest lower bound or meet).An example is given by the power set of a set, partially ordered by …

Order, an academic journal on order theory; Order (mathematics), Order, an arrangement of items in sequence; Order, the result of enumeration of a set of items; Order, a mathematical structure modeling sequenced items, dealt with in order theory; Order of hierarchical complexity, quantified by the model of hierarchical complexity, the ordinal ...

In order-theoretic mathematics, a series-parallel partial order is a partially ordered set built up from smaller series-parallel partial orders by two simple composition operations.. The series-parallel partial orders may be characterized as the N-free finite partial orders; they have order dimension at most two. They include weak orders and the reachability relationship in directed …

Breadth-first search (BFS) is an algorithm for searching a tree data structure for a node that satisfies a given property. It starts at the tree root and explores all nodes at the present depth prior to moving on to the nodes at the next depth level. Extra memory, usually a queue, is needed to keep track of the child nodes that were encountered but not yet explored.

The first-order theory of total orders is decidable, i.e. there is an algorithm for deciding which first-order statements hold for all total orders. Using interpretability in S2S, the monadic second-order theory of countable total orders is also decidable. [citation needed] Orders on the Cartesian product of totally ordered sets

In physics, the relativity of simultaneity is the concept that distant simultaneity – whether two spatially separated events occur at the same time – is not absolute, but depends on the observer's reference frame.This possibility was raised by mathematician Henri Poincaré in 1900, and thereafter became a central idea in the special theory of relativity

In mathematical analysis, asymptotic analysis, also known as asymptotics, is a method of describing limiting behavior.. As an illustration, suppose that we are interested in the properties of a function f (n) as n becomes very large. If f(n) = n 2 + 3n, then as n becomes very large, the term 3n becomes insignificant compared to n 2.The function f(n) is said to be "asymptotically …

Historical approaches. In its original form during the Medieval period of European warfare, an order of battle was the order in which troops were positioned relative to the position of the army commander. The term was also applied to the disposition of ships in the line of battle during the age of sail.In the later transformation of its meaning during the European period of Early …