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Euler Diagram
An Euler diagram (, ) is a diagrammatic means of representing Set (mathematics), sets and their relationships. They are particularly useful for explaining complex hierarchies and overlapping definitions. They are similar to another set diagramming technique, Venn diagrams. Unlike Venn diagrams, which show all possible relations between different sets, the Euler diagram shows only relevant relationships. The first use of "Eulerian circles" is commonly attributed to Swiss mathematician Leonhard Euler (1707–1783). In the United States, both Venn and Euler diagrams were incorporated as part of instruction in set theory as part of the new math movement of the 1960s. Since then, they have also been adopted by other curriculum fields such as reading as well as organizations and businesses. Euler diagrams consist of simple closed shapes in a two-dimensional plane that each depict a set or category. How or whether these shapes overlap demonstrates the relationships between the sets. Ea ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Christian Weise
Christian Weise (30 April 1642 – 21 October 1708), also known under the pseudonyms Siegmund Gleichviel, Orontes, Catharinus Civilis and Tarquinius Eatullus, was a German writer, dramatist, poet, pedagogue and librarian of the Baroque era. He produced a large number of dramatic works, noted for their social criticism and idiomatic style. In the 1670s he started a fashion for German "political novels". He has also been credited with the invention of the mathematical Euler diagram, though this is uncertain. Biography Christian Weise was born in Zittau, the son of Elias Weise, a ''magister tertium'' or assistant teacher. Weise studied theology at the University of Leipzig, gaining a Magister's degree in 1663. His studies expanded into rhetoric, politics, history and poetry, and for a brief period after his graduation he lectured there in those subjects. However, in 1668 he secured a post at the court in Halle, as the secretary of Simon Philipp von Leiningen-Westerburg, the ministe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Edward W
Edward is an English language, English male name. It is derived from the Old English, Anglo-Saxon name ''Ēadweard'', composed of the elements ''wikt:ead#Old English, ēad'' "wealth, fortunate; prosperous" and ''wikt:weard#Old English, weard'' "guardian, protector”. History The name Edward was very popular in Anglo-Saxon England, but the rule of the House of Normandy, Norman and House of Plantagenet, Plantagenet dynasties had effectively ended its use amongst the upper classes. The popularity of the name was revived when Henry III of England, Henry III named his firstborn son, the future Edward I of England, Edward I, as part of his efforts to promote a cult around Edward the Confessor, for whom Henry had a deep admiration. Variant forms The name has been adopted in the Iberian Peninsula#Modern Iberia, Iberian peninsula since the 15th century, due to Edward, King of Portugal, whose mother was English. The Spanish/Portuguese forms of the name are Eduardo and Duarte (name), Duart ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Maurice Karnaugh
Maurice Karnaugh (; October 4, 1924 – November 8, 2022) was an American physicist, mathematician, computer scientist, and inventor known for the Karnaugh map used in Boolean algebra. Early life and education Karnaugh earned a B.A in physics from the City College of New York in 1948 and a PhD. in physics from Yale in 1952. He later studied mathematics and physics at City College of New York (1944 to 1948) and transferred to Yale University to complete his B.Sc. (1949), M.Sc. (1950) and Ph.D. in physics with a thesis on ''The Theory of Magnetic Resonance and Lambda-Type Doubling in Nitric-Oxide'' (1952). Career Karnaugh worked at Bell Labs and IBM from 1952 to 1993. From 1980 until 1999 Karnaugh taught computer science at Polytechnic University of New York. At Bell Labs, (1952 to 1966), developing the Karnaugh map (1954) as well as patents for PCM encoding and magnetic logic circuits and coding. He later worked at IBM's Federal Systems Division in Gaithersburg (1966 to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Domain Of Discourse
In the formal sciences, the domain of discourse or universe of discourse (borrowing from the mathematical concept of ''universe'') is the set of entities over which certain variables of interest in some formal treatment may range. It is also defined as the collection of objects being discussed in a specific discourse. In model-theoretical semantics, a universe of discourse is the set of entities that a model is based on. The domain of discourse is usually identified in the preliminaries, so that there is no need in the further treatment to specify each time the range of the relevant variables. Many logicians distinguish, sometimes only tacitly, between the ''domain of a science'' and the ''universe of discourse of a formalization of the science''. Etymology The concept ''universe of discourse'' was used for the first time by George Boole (1854) on page 42 of his '' Laws of Thought'': The concept, probably discovered independently by Boole in 1847, played a crucial role i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Louis Couturat
Louis Couturat (; 17 January 1868 – 3 August 1914) was a French logician, mathematician, philosopher, and linguist. Couturat was a pioneer of the constructed language Ido. Life and education Born in Paris. In 1887 he entered École Normale Supérieure to study philosophy and mathematics. In 1895 he lectured in philosophy at the University of Toulouse and 1897 lectured in philosophy of mathematics at the University of Caen Normandy, taking a stand in favor of transfinite numbers. After a time in Hanover studying the writings of Leibniz, he became an assistant to Henri-Louis Bergson at the Collège de France in 1905. Career He was the French advocate of the symbolic logic that emerged in the years before World War I, thanks to the writings of Charles Sanders Peirce, Giuseppe Peano and his school, and especially to ''The Principles of Mathematics'' by Couturat's friend and correspondent Bertrand Russell. Like Russell, Couturat saw symbolic logic as a tool to advance both ma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Venn Diagrams
A Venn diagram is a widely used diagram style that shows the logical relation between sets, popularized by John Venn (1834–1923) in the 1880s. The diagrams are used to teach elementary set theory, and to illustrate simple set relationships in probability, logic, statistics, linguistics and computer science. A Venn diagram uses simple closed curves on a plane to represent sets. The curves are often circles or ellipses. Similar ideas had been proposed before Venn such as by Christian Weise in 1712 (''Nucleus Logicoe Wiesianoe'') and Leonhard Euler in 1768 ('' Letters to a German Princess''). The idea was popularised by Venn in ''Symbolic Logic'', Chapter V "Diagrammatic Representation", published in 1881. Details A Venn diagram, also called a ''set diagram'' or ''logic diagram'', shows ''all'' possible logical relations between a finite collection of different sets. These diagrams depict elements as points in the plane, and sets as regions inside closed curves. A Venn d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algorithm
In mathematics and computer science, an algorithm () is a finite sequence of Rigour#Mathematics, mathematically rigorous instructions, typically used to solve a class of specific Computational problem, problems or to perform a computation. Algorithms are used as specifications for performing calculations and data processing. More advanced algorithms can use Conditional (computer programming), conditionals to divert the code execution through various routes (referred to as automated decision-making) and deduce valid inferences (referred to as automated reasoning). In contrast, a Heuristic (computer science), heuristic is an approach to solving problems without well-defined correct or optimal results.David A. Grossman, Ophir Frieder, ''Information Retrieval: Algorithms and Heuristics'', 2nd edition, 2004, For example, although social media recommender systems are commonly called "algorithms", they actually rely on heuristics as there is no truly "correct" recommendation. As an e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Venn 1881 P 115-116 Pasteup
Venn is a surname and a given name. It may refer to: Given name * Venn Eyre (died 1777), Archdeacon of Carlisle, Cumbria, England * Venn Pilcher (1879–1961), Anglican bishop, writer, and translator of hymns * Venn Young (1929–1993), New Zealand politician Surname * Albert Venn (1867–1908), American lacrosse player * Anne Venn (1620s–1654), English religious radical and diarist * Blair Venn, Australian actor * Charles Venn (born 1973), British actor * Harry Venn (1844–1908), Australian politician * Henry Venn (Church Missionary Society) (1796-1873), secretary of the Church Missionary Society, grandson of Henry Venn * Henry Venn (Clapham Sect) (1725–1797), English evangelical minister * Horace Venn (1892–1953), English cricketer * John Venn (1834–1923), British logician and the inventor of Venn diagrams, son of Henry Venn the younger * John Venn (academic) (died 1687), English academic administrator * John Venn (politician) (1586–1650), English politician * Jo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Venn
John Venn, Fellow of the Royal Society, FRS, Fellow of the Society of Antiquaries of London, FSA (4 August 1834 – 4 April 1923) was an English mathematician, logician and philosopher noted for introducing Venn diagrams, which are used in logic, set theory, probability, statistics, and computer science. In 1866, Venn published ''The Logic of Chance'', a groundbreaking book which espoused the frequency theory of probability, arguing that probability should be determined by how often something is forecast to occur as opposed to "educated" assumptions. Venn then further developed George Boole's theories in the 1881 work ''Symbolic Logic'', where he highlighted what would become known as Venn diagrams. Early life John Venn was born on 4 August 1834 in Kingston upon Hull, Yorkshire, to Martha Sykes and Rev. Henry Venn (Church Missionary Society), Henry Venn, who was the rector of the parish of Drypool. His mother died when he was three years old. Venn was descended from a long ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Syllogism
A syllogism (, ''syllogismos'', 'conclusion, inference') is a kind of logical argument that applies deductive reasoning to arrive at a conclusion based on two propositions that are asserted or assumed to be true. In its earliest form (defined by Aristotle in his 350 BC book '' Prior Analytics''), a deductive syllogism arises when two true premises (propositions or statements) validly imply a conclusion, or the main point that the argument aims to get across. For example, knowing that all men are mortal (major premise), and that Socrates is a man (minor premise), we may validly conclude that Socrates is mortal. Syllogistic arguments are usually represented in a three-line form: All men are mortal. Socrates is a man. Therefore, Socrates is mortal.In antiquity, two rival syllogistic theories existed: Aristotelian syllogism and Stoic syllogism. From the Middle Ages onwards, ''categorical syllogism'' and ''syllogism'' were usually used interchangeably. This article is concern ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Categorical Proposition
In logic, a categorical proposition, or categorical statement, is a proposition that asserts or denies that all or some of the members of one category (the ''subject term'') are included in another (the ''predicate term''). The study of arguments using categorical statements (i.e., syllogisms) forms an important branch of deductive reasoning that began with the Ancient Greeks. The Ancient Greeks such as Aristotle identified four primary distinct types of categorical proposition and gave them standard forms (now often called ''A'', ''E'', ''I'', and ''O''). If, abstractly, the subject category is named ''S'' and the predicate category is named ''P'', the four standard forms are: * All ''S'' are ''P''. (''A'' form) * No ''S'' are ''P''. (''E'' form) * Some ''S'' are ''P''. (''I'' form) * Some ''S'' are not ''P''. (''O'' form) A large number of sentences may be translated into one of these canonical forms while retaining all or most of the original meaning of the sentence. Greek inves ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
