|
Axioms Of Set Theory
Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory – as a branch of mathematics – is mostly concerned with those that are relevant to mathematics as a whole. The modern study of set theory was initiated by the German mathematicians Richard Dedekind and Georg Cantor in the 1870s. In particular, Georg Cantor is commonly considered the founder of set theory. The non-formalized systems investigated during this early stage go under the name of ''naive set theory''. After the discovery of paradoxes within naive set theory (such as Russell's paradox, Cantor's paradox and the Burali-Forti paradox), various axiomatic systems were proposed in the early twentieth century, of which Zermelo–Fraenkel set theory (with or without the axiom of choice) is still the best-known and most studied. Set theory is commonly employed as a foundation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Venn A Intersect B
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 * John V ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Philosophy
Philosophy ('love of wisdom' in Ancient Greek) is a systematic study of general and fundamental questions concerning topics like existence, reason, knowledge, Value (ethics and social sciences), value, mind, and language. It is a rational and critical inquiry that reflects on its methods and assumptions. Historically, many of the individual sciences, such as physics and psychology, formed part of philosophy. However, they are considered separate academic disciplines in the modern sense of the term. Influential traditions in the history of philosophy include Western philosophy, Western, Islamic philosophy, Arabic–Persian, Indian philosophy, Indian, and Chinese philosophy. Western philosophy originated in Ancient Greece and covers a wide area of philosophical subfields. A central topic in Arabic–Persian philosophy is the relation between reason and revelation. Indian philosophy combines the Spirituality, spiritual problem of how to reach Enlightenment in Buddhism, enlighten ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Paradoxes Of The Infinite
''Paradoxes of the Infinite'' (German title: ''Paradoxien des Unendlichen'') is a mathematical work by Bernard Bolzano on the theory of sets. It was published by a friend and student, František Přihonský, in 1851, three years after Bolzano's death. The work contained many interesting results in set theory. Bolzano expanded on the theme of Galileo's paradox, giving more examples of correspondences between the elements of an infinite set and proper subset In mathematics, a set ''A'' is a subset of a set ''B'' if all elements of ''A'' are also elements of ''B''; ''B'' is then a superset of ''A''. It is possible for ''A'' and ''B'' to be equal; if they are unequal, then ''A'' is a proper subset ...s of infinite sets. In the work he also explained the term ''Menge'', rendered in English as "set", which he had coined and used in several works since the 1830s. References * ''Paradoxes of the Infinite''; trans. by D.A.Steele; London: Routledge, 1950 * (German original) * ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bernard Bolzano
Bernard Bolzano (, ; ; ; born Bernardus Placidus Johann Nepomuk Bolzano; 5 October 1781 – 18 December 1848) was a Bohemian mathematician, logician, philosopher, theologian and Catholic priest of Italian extraction, also known for his liberal views. Bolzano wrote in German, his native language. For the most part, his work came to prominence posthumously. Family Bolzano was the son of two pious Catholics. His father, Bernard Pompeius Bolzano, was an Italian who had moved to Prague, where he married Maria Cecilia Maurer who came from Prague's German-speaking family Maurer. Only two of their twelve children lived to adulthood. Career When he was ten years old, Bolzano entered the Gymnasium of the Piarists in Prague, which he attended from 1791 to 1796. Bolzano entered the University of Prague in 1796 and studied mathematics, philosophy and physics. Starting in 1800, he also began studying theology, becoming a Catholic priest in 1804. He was appointed to the new chair of p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tree Of Porphyry
In philosophy (particularly the theory of categories), the Porphyrian tree or Tree of Porphyry is a classic device for illustrating a "scale of being" (), attributed to the 3rd-century CE Greek neoplatonist philosopher and logician Porphyry, and revived through the translations of Boethius. Porphyry suggests the tree in his introduction ("") to Aristotle's Categories. Porphyry presented Aristotle's classification of categories in a way that was later adopted into tree-like diagrams of two-way divisions, which indicate that a species is defined by a genus and a differentia and that this logical process continues until the lowest species is reached, which can no longer be so defined. No illustrations or diagrams occur in editions of Porphyry's original work; diagrams were eventually made, and became associated with the scheme that Porphyry describes, following Aristotle. Porphyry's was originally written in Greek, but was translated into Latin in the early 6th century CE by Bo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
