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∧ B, Y
Wedge (∧) is a symbol that looks similar to an in-line caret (^). It is used to represent various operations. In Unicode, the symbol is encoded and by \wedge and \land in TeX. The opposite symbol (∨) is called a vel, or sometimes a (descending) wedge. Some authors who call the descending wedge ''vel'' often call the ascending wedge ''ac'' (the corresponding Latin word for "and", also spelled "atque"), keeping their usage parallel Use Wedge is used to represent various operations: * Logical conjunction in propositional logic and first-order logic * Meet in lattice theory * Exterior product or wedge product in differential geometry Differential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of differential calculus, integral calculus, linear algebra and multili ... See also * Turned v * Vel (symbol) * List of mathematical symbols * List of logic sym ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Symbol
A symbol is a mark, sign, or word that indicates, signifies, or is understood as representing an idea, object, or relationship. Symbols allow people to go beyond what is known or seen by creating linkages between otherwise very different concepts and experiences. All communication (and data processing) is achieved through the use of symbols. Symbols take the form of words, sounds, gestures, ideas, or visual images and are used to convey other ideas and beliefs. For example, a red octagon is a common symbol for "STOP"; on maps, blue lines often represent rivers; and a red rose often symbolizes love and compassion. Numerals are symbols for numbers; letters of an alphabet may be symbols for certain phonemes; and personal names are symbols representing individuals. The variable 'x', in a mathematical equation, may symbolize the position of a particle in space. The academic study of symbols is semiotics. In cartography, an organized collection of symbols forms a legend for a map ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lattice (order)
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 inclusion, for which the supremum is the union and the infimum is the intersection. Another example is given by the natural numbers, partially ordered by divisibility, for which the supremum is the least common multiple and the infimum is the greatest common divisor. Lattices can also be characterized as algebraic structures satisfying certain axiomatic identities. Since the two definitions are equivalent, lattice theory draws on both order theory and universal algebra. Semilattices include lattices, which in turn include Heyting and Boolean algebras. These ''lattice-like'' structures all admi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wedge (other)
A wedge is a triangular-shaped simple machine. Wedge, The Wedge, or Wedges may also refer to: Common meanings * Wedge (footwear), a type of shoe * Wedge (golf), a type of golf club Culture Fictional characters * Wedge (''Transformers''), an Autobot, leader of the Build Team in the "Transformers: Robots in Disguise" toy line * Wedge Antilles, a character in the ''Star Wars'' films * Wedge, a recurring character in the ''Final Fantasy'' video game series; see Biggs and Wedge Music * ''The Wedge'' (album), by the British band Pallas * "The Wedge" (song), by American band Phish, 1993 * Prelude and Fugue in E minor, BWV 548, a work by Johann Sebastian Bach sometimes called "The Wedge" * Wedge Records, a record label Television * ''The Wedge'' (Australian TV series), a sketch show on Network Ten, aired until 2007 * ''The Wedge'' (Canadian TV series), a music show on MuchMusic, aired until 2014 Publications * ''The Wedge'' (poetry), a collection by William Carlos Williams * ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
List Of Logic Symbols
In logic, a set of symbols is commonly used to express logical representation. The following table lists many common symbols, together with their name, how they should be read out loud, and the related field of mathematics. Additionally, the subsequent columns contains an informal explanation, a short example, the Unicode location, the name for use in HTML documents, and the LaTeX symbol. Basic logic symbols Advanced and rarely used logical symbols These symbols are sorted by their Unicode value: Usage in various countries Poland and Germany in Poland, the universal quantifier is sometimes written ∧, and the existential quantifier as ∨. The same applies for Germany. Japan The ⇒ symbol is often used in text to mean "result" or "conclusion", as in "We examined whether to sell the product ⇒ We will not sell it". Also, the → symbol is often used to denote "changed to", as in the sentence "The interest rate changed. March 20% → April 21%". See also * Józef ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
List Of Mathematical Symbols
A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation between mathematical objects, or for structuring the other symbols that occur in a formula. As formulas are entirely constituted with symbols of various types, many symbols are needed for expressing all mathematics. The most basic symbols are the decimal digits (0, 1, 2, 3, 4, 5, 6, 7, 8, 9), and the letters of the Latin alphabet. The decimal digits are used for representing numbers through the Hindu–Arabic numeral system. Historically, upper-case letters were used for representing points in geometry, and lower-case letters were used for variables and constants. Letters are used for representing many other sorts of mathematical objects. As the number of these sorts has remarkably increased in modern mathematics, the Greek alphabet and some Hebrew letters are also used. In mathematical formulas, the standard typeface is ital ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Differential Geometry
Differential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of differential calculus, integral calculus, linear algebra and multilinear algebra. The field has its origins in the study of spherical geometry as far back as antiquity. It also relates to astronomy, the geodesy of the Earth, and later the study of hyperbolic geometry by Lobachevsky. The simplest examples of smooth spaces are the plane and space curves and surfaces in the three-dimensional Euclidean space, and the study of these shapes formed the basis for development of modern differential geometry during the 18th and 19th centuries. Since the late 19th century, differential geometry has grown into a field concerned more generally with geometric structures on differentiable manifolds. A geometric structure is one which defines some notion of size, distance, shape, volume, or other rigidifying structu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Exterior Algebra
In mathematics, the exterior algebra, or Grassmann algebra, named after Hermann Grassmann, is an algebra that uses the exterior product or wedge product as its multiplication. In mathematics, the exterior product or wedge product of vectors is an algebraic construction used in geometry to study areas, volumes, and their higher-dimensional analogues. The exterior product of two vectors u and v, denoted by u \wedge v, is called a bivector and lives in a space called the ''exterior square'', a vector space that is distinct from the original space of vectors. The magnitude of u \wedge v can be interpreted as the area of the parallelogram with sides u and v, which in three dimensions can also be computed using the cross product of the two vectors. More generally, all parallel plane surfaces with the same orientation and area have the same bivector as a measure of their oriented area. Like the cross product, the exterior product is anticommutative, meaning t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Join And Meet
In mathematics, specifically order theory, the join of a subset S of a partially ordered set P is the supremum (least upper bound) of S, denoted \bigvee S, and similarly, the meet of S is the infimum (greatest lower bound), denoted \bigwedge S. In general, the join and meet of a subset of a partially ordered set need not exist. Join and meet are dual to one another with respect to order inversion. A partially ordered set in which all pairs have a join is a join-semilattice. Dually, a partially ordered set in which all pairs have a meet is a meet-semilattice. A partially ordered set that is both a join-semilattice and a meet-semilattice is a lattice. A lattice in which every subset, not just every pair, possesses a meet and a join is a complete lattice. It is also possible to define a partial lattice, in which not all pairs have a meet or join but the operations (when defined) satisfy certain axioms. The join/meet of a subset of a totally ordered set is simply the maximal/m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Caret
Caret is the name used familiarly for the character , provided on most QWERTY keyboards by typing . The symbol has a variety of uses in programming and mathematics. The name "caret" arose from its visual similarity to the original proofreader's caret, a mark used in proofreading to indicate where a punctuation mark, word, or phrase should be inserted into a document. The formal ASCII standard (X3.64.1977) calls it a "circumflex". History Typewriters On typewriters designed for languages that routinely use diacritics (accent marks), there are two possible ways to type these. Keys can be dedicated to precomposed characters (with the diacritic included) or alternatively a dead key mechanism can be provided. With the latter, a mark is made when a dead key is typed but, unlike normal keys, the paper carriage does not move on and thus the next letter to be typed is printed under the accent. The symbol was originally provided in typewriters and computer printers so that circumfl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
First-order Logic
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 is a man", one can have expressions in the form "there exists x such that x is Socrates and x is a man", where "there exists''"'' is a quantifier, while ''x'' is a variable. This distinguishes it from propositional logic, which does not use quantifiers or relations; in this sense, propositional logic is the foundation of first-order logic. A theory about a topic is usually a first-order logic together with a specified domain of discourse (over which the quantified variables range), finitely many functions from that domain to itself, finitely many predicates defined on that domain, and a set of ax ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Propositional Calculus
Propositional calculus is a branch of logic. It is also called propositional logic, statement logic, sentential calculus, sentential logic, or sometimes zeroth-order logic. It deals with propositions (which can be true or false) and relations between propositions, including the construction of arguments based on them. Compound propositions are formed by connecting propositions by logical connectives. Propositions that contain no logical connectives are called atomic propositions. Unlike first-order logic, propositional logic does not deal with non-logical objects, predicates about them, or Quantifier (logic), quantifiers. However, all the machinery of propositional logic is included in first-order logic and higher-order logics. In this sense, propositional logic is the foundation of first-order logic and higher-order logic. Explanation Logical connectives are found in natural languages. In English for example, some examples are "and" (logical conjunction, conjunction), "or" (lo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
