Total orderIn mathematics, a total order or linear order is a partial order in which any two elements are comparable. That is, a total order is a binary relation on some set , which satisfies the following for all and in : (reflexive). If and then (transitive). If and then (antisymmetric). or (strongly connected, formerly called total). Reflexivity (1.) already follows from connectedness (4.), but is required explicitly by many authors nevertheless, to indicate the kinship to partial orders.
Lexicographic orderIn mathematics, the lexicographic or lexicographical order (also known as lexical order, or dictionary order) is a generalization of the alphabetical order of the dictionaries to sequences of ordered symbols or, more generally, of elements of a totally ordered set. There are several variants and generalizations of the lexicographical ordering. One variant applies to sequences of different lengths by comparing the lengths of the sequences before considering their elements.
Order isomorphismIn the mathematical field of order theory, an order isomorphism is a special kind of monotone function that constitutes a suitable notion of isomorphism for partially ordered sets (posets). Whenever two posets are order isomorphic, they can be considered to be "essentially the same" in the sense that either of the orders can be obtained from the other just by renaming of elements. Two strictly weaker notions that relate to order isomorphisms are order embeddings and Galois connections.
Port forwardingIn computer networking, port forwarding or port mapping is an application of network address translation (NAT) that redirects a communication request from one address and port number combination to another while the packets are traversing a network gateway, such as a router or firewall. This technique is most commonly used to make services on a host residing on a protected or masqueraded (internal) network available to hosts on the opposite side of the gateway (external network), by remapping the destination IP address and port number of the communication to an internal host.
Link-local addressIn computer networking, a link-local address is a unicast network address that is valid only for communications within the subnetwork that the host is connected to. Link-local addresses are most often assigned automatically with a process known as stateless address autoconfiguration or link-local address autoconfiguration, also known as automatic private IP addressing (APIPA) or auto-IP. Link-local addresses are not guaranteed to be unique beyond their network segment.
Network address translationNetwork address translation (NAT) is a method of mapping an IP address space into another by modifying network address information in the IP header of packets while they are in transit across a traffic routing device. The technique was originally used to bypass the need to assign a new address to every host when a network was moved, or when the upstream Internet service provider was replaced, but could not route the network's address space. It has become a popular and essential tool in conserving global address space in the face of IPv4 address exhaustion.
Computer simulationComputer simulation is the process of mathematical modelling, performed on a computer, which is designed to predict the behaviour of, or the outcome of, a real-world or physical system. The reliability of some mathematical models can be determined by comparing their results to the real-world outcomes they aim to predict. Computer simulations have become a useful tool for the mathematical modeling of many natural systems in physics (computational physics), astrophysics, climatology, chemistry, biology and manufacturing, as well as human systems in economics, psychology, social science, health care and engineering.
Simulation video gameSimulation video games are a diverse super-category of video games, generally designed to closely simulate real world activities. A simulation game attempts to copy various activities from real life in the form of a game for various purposes such as training, analysis, prediction, or entertainment. Usually there are no strictly defined goals in the game, and the player is allowed to control a character or environment freely. Well-known examples are war games, business games, and role play simulation.
Social mobilitySocial mobility is the movement of individuals, families, households or other categories of people within or between social strata in a society. It is a change in social status relative to one's current social location within a given society. This movement occurs between layers or tiers in an open system of social stratification. Open stratification systems are those in which at least some value is given to achieved status characteristics in a society. The movement can be in a downward or upward direction.
Order theoryOrder 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 order theory glossary. Orders are everywhere in mathematics and related fields like computer science. The first order often discussed in primary school is the standard order on the natural numbers e.
