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∧
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 See also * Turned v * Vel (symbol) * List of mathematical symbols *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 sub . ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
First-order Logic
First-order logic, also called predicate logic, predicate calculus, or quantificational logic, 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. Rather than propositions such as "all humans are mortal", in first-order logic one can have expressions in the form "for all ''x'', if ''x'' is a human, then ''x'' is mortal", where "for all ''x"'' is a quantifier, ''x'' is a variable, and "... ''is a human''" and "... ''is mortal''" are predicates. 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, such as set theory, a theory for groups,A. Tarski, ''Undecidable Theories'' (1953), p. 77. Studies in Logic and the Foundation of Mathematics, North-Holland or a formal theory o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Exterior Algebra
In mathematics, the exterior algebra or Grassmann algebra of a vector space V is an associative algebra that contains V, which has a product, called exterior product or wedge product and denoted with \wedge, such that v\wedge v=0 for every vector v in V. The exterior algebra is named after Hermann Grassmann, and the names of the product come from the "wedge" symbol \wedge and the fact that the product of two elements of V is "outside" V. The wedge product of k vectors v_1 \wedge v_2 \wedge \dots \wedge v_k is called a ''blade (geometry), blade of degree k'' or ''k-blade''. The wedge product was introduced originally as an algebraic construction used in geometry to study areas, volumes, and their higher-dimensional analogues: the magnitude (mathematics), magnitude of a bivector, -blade v\wedge w is the area of the parallelogram defined by v and w, and, more generally, the magnitude of a k-blade is the (hyper)volume of the Parallelepiped#Parallelotope, parallelotope defined by the ... [...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 or a mathematical expression. More formally, a ''mathematical symbol'' is any grapheme used in mathematical formulas and expressions. As formulas and expressions 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 types of mathematical object. As the number of these types has increased, ... [...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 or rarely used logical symbols The following symbols are either advanced and context-sensitive or very rarely used: See also * Glossary of logic * Józef Maria Bocheński * List of notation used in Principia Mathematica * List of mathematical symbols * Logic alphabet, a suggested set of logical symbols * * Logical connective * Mathematical operators and symbols in Unicode * Non-logical symbol * Polish notation * Truth function * Truth table * Wikipedia:WikiProject Logic/Standards for notation References Further reading * Józef Maria Bocheński ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
/\ (other) , a V-shaped mark, often inverted
{{disambiguation ...
/\ may refer to: * Λ, uppercase lambda, the 11th letter of the Greek alphabet * /\, ASCII symbol for boolean "and" operator, formed with a slash and a backslash * /\, an ALGOL 68 boolean "and" operator * /\, the boolean "and" operator in early K&R C in Unix V6, Unix V7 and more recently BSD 2.11 * ∧, the wedge symbol, used for logical conjunction * ^, the caret symbol See also * Chevron (insignia) A chevron (also spelled cheveron, especially in older documents) is a V-shaped mark or symbol, often inverted. The word is usually used in reference to a kind of fret in architecture, or to a badge or insignia used in military or police unifo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logical Conjunction
In logic, mathematics and linguistics, ''and'' (\wedge) is the Truth function, truth-functional operator of conjunction or logical conjunction. The logical connective of this operator is typically represented as \wedge or \& or K (prefix) or \times or \cdot in which \wedge is the most modern and widely used. The ''and'' of a set of operands is true if and only if ''all'' of its operands are true, i.e., A \land B is true if and only if A is true and B is true. An operand of a conjunction is a conjunct. Beyond logic, the term "conjunction" also refers to similar concepts in other fields: * In natural language, the denotation of expressions such as English language, English "Conjunction (grammar), and"; * In programming languages, the Short-circuit evaluation, short-circuit and Control flow, control structure; * In set theory, Intersection (set theory), intersection. * In Lattice (order), lattice theory, logical conjunction (Infimum and supremum, greatest lower bound). Notati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Turned V
Turned v (majuscule: Ʌ, minuscule: ʌ) is a letter of the Latin alphabet, based on a turned form of the letter V. It is used in the orthographies of Dan, Ch’ol, Nankina, Northern Tepehuán, Temne, Oneida, and Wounaan and also some orthographies of Ibibio. Its lowercase is used in the International Phonetic Alphabet to represent an open-mid back unrounded vowel, the vowel in ''plus'' in many dialects of English. Despite the similarity in appearance, the letter has no connection to the Greek Λ, Cyrillic Л, CJK radical 人, or Korean ㅅ. In German and French handwriting, the numeral 1 often takes the form of a turned V, whereby the serif is extended down to the length of the main stroke. Character encoding Related characters Descendants and related letters in the Latin alphabet *ʌ with diacritics: ʌ́ ʌ̀ *ᶺ : Modifier letter small turned v is used in phonetic transcription See also Similar symbols: * Caron * Caret * Circumflex * Logical conjun ... [...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 ASCII standard (X3.64.1977) calls it a "circumflex"; the Unicode standard calls it a "circumflex accent", although it is no longer practicable for that purpose. 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); 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 ... [...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 * ''The Wedge'' (Canadian TV series), a music show on MuchMusic Publications * ''The Wedge'' (poetry collection), 1944 collection of poems by William Carlos Williams * '' Wedge: Th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Differential Geometry
Differential geometry is a Mathematics, mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of Calculus, single variable calculus, vector calculus, linear algebra and multilinear algebra. The field has its origins in the study of spherical geometry as far back as classical antiquity, antiquity. It also relates to astronomy, the geodesy of the Earth, and later the study of hyperbolic geometry by Nikolai Lobachevsky, Lobachevsky. The simplest examples of smooth spaces are the Differential geometry of curves, plane and space curves and Differential geometry of surfaces, 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Symbol
A symbol is a mark, Sign (semiotics), sign, or word that indicates, signifies, or is understood as representing an idea, physical object, object, or wikt:relationship, relationship. Symbols allow people to go beyond what is known or seen by creating linkages between otherwise different concepts and experiences. All communication is achieved through the use of symbols: for example, a red octagon is a common symbol for "Stop sign, STOP"; on maps, blue lines often represent rivers; and a red rose often symbolizes love and compassion. Numerical digit, Numerals are symbols for numbers; Letter (alphabet), letters of an alphabet may be symbols for certain phonemes; and personal names are symbols representing individuals. The academic study of symbols is called semiotics. In the arts, Artistic symbol, symbolism is the use of a abstract and concrete, concrete element to represent a more abstract idea. In cartography, an organized collection of symbols forms a map layout, legend for a ma ... [...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 (mathematics), join) and a unique infimum (also called a greatest lower bound or meet (mathematics), meet). An example is given by the power set of a set, partially ordered by Subset, inclusion, for which the supremum is the Union (set theory), union and the infimum is the Intersection (set theory), 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 Identity (mathematics), identities. Since the two definitions are equivalent, lattice theory draws on both order theory and universal algebra. Semilatti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
