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.
Order topologyIn mathematics, an order topology is a certain topology that can be defined on any totally ordered set. It is a natural generalization of the topology of the real numbers to arbitrary totally ordered sets. If X is a totally ordered set, the order topology on X is generated by the subbase of "open rays" for all a, b in X. Provided X has at least two elements, this is equivalent to saying that the open intervals together with the above rays form a base for the order topology.
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.
IntellectIn the study of the human mind, intellect is the ability of the human mind to reach correct conclusions about what is true and what is false in reality; and how to solve problems. Translated from the Ancient Greek philosophical concept nous, intellect derived from the Latin intelligere (“to understand”), from which the term intelligence in the French and English languages is also derived. The discussion of intellect can be divided into two areas that concern the relation between intelligence and intellect.
Active intellectIn medieval philosophy, the active intellect (Latin: intellectus agens; also translated as agent intellect, active intelligence, active reason, or productive intellect) is the formal (morphe) aspect of the intellect (nous), according to the Aristotelian theory of hylomorphism. The nature of the active intellect was a major theme of late classical and medieval philosophy. Various thinkers sought to reconcile their commitment to Aristotle's account of the body and soul to their own theological commitments.
ArchitectureArchitecture is the art and technique of designing and building, as distinguished from the skills associated with construction. It is both the process and the product of sketching, conceiving, planning, designing, and constructing buildings or other structures. The term comes ; ; . Architectural works, in the material form of buildings, are often perceived as cultural symbols and as works of art. Historical civilizations are often identified with their surviving architectural achievements.
ExperienceExperience refers to conscious events in general, more specifically to perceptions, or to the practical knowledge and familiarity that is produced by these processes. Understood as a conscious event in the widest sense, experience involves a subject to which various items are presented. In this sense, seeing a yellow bird on a branch presents the subject with the objects "bird" and "branch", the relation between them and the property "yellow". Unreal items may be included as well, which happens when experiencing hallucinations or dreams.
New Classical architectureNew Classical architecture, New Classicism or Contemporary Classical architecture is a contemporary movement in architecture that continues the practice of Classical architecture. It is sometimes considered the modern continuation of Neoclassical architecture, even though other styles might be cited as well, such as Gothic, Baroque, Renaissance or even non-Western styles – often referenced and recreated from a postmodern perspective as opposed to being strict revival styles.
