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Peano Models
Giuseppe Peano (; ; 27 August 1858 – 20 April 1932) was an Italian mathematician and glottologist. The author of over 200 books and papers, he was a founder of mathematical logic and set theory, to which he contributed much notation. The standard axiomatization of the natural numbers is named the Peano axioms in his honor. As part of this effort, he made key contributions to the modern rigorous and systematic treatment of the method of mathematical induction. He spent most of his career teaching mathematics at the University of Turin. He also wrote an international auxiliary language, Latino sine flexione ("Latin without inflections"), which is a simplified version of Classical Latin. Most of his books and papers are in Latino sine flexione, others are in Italian. Biography Peano was born and raised on a farm at Spinetta, a hamlet now belonging to Cuneo, Piedmont, Italy. He attended the Liceo classico Cavour in Turin, and enrolled at the University of Turin in 1876, graduating ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cuneo
Cuneo (; pms, Coni ; oc, Coni/Couni ; french: Coni ) is a city and ''comune'' in Piedmont, Northern Italy, the capital of the province of Cuneo, the fourth largest of Italy’s provinces by area. It is located at 550 metres (1,804 ft) in the south-west of Piedmont, at the confluence of the rivers Stura and Gesso. Cuneo is bounded by the municipalities of Beinette, Borgo San Dalmazzo, Boves, Busca, Caraglio, Castelletto Stura, Centallo, Cervasca, Morozzo, Peveragno, Tarantasca and Vignolo. It is located near six mountain passes: *Colle della Maddalena at *Colle di Tenda at – Tunnel of Tenda at , long *Colle del Melogno at *Colle San Bernardo at *Colle di Nava at * Colle di Cadibona at . History Cuneo was founded in 1198 by the local population, who declared it an independent commune, freeing themselves from the authority of the bishops of Asti and the marquisses of Montferrat and Saluzzo. In 1210, the latter occupied it, and in 1231 the ''Cuneesi'' rebe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Peano–Russell Notation
In mathematical logic, Peano–Russell notation was Bertrand Russell's application of Giuseppe Peano's logical notation to the logical notions of Frege and was used in the writing of ''Principia Mathematica'' in collaboration with Alfred North Whitehead: "The notation adopted in the present work is based upon that of Peano, and the following explanations are to some extent modelled on those which he prefixes to his ''Formulario Mathematico''." (Chapter I: Preliminary Explanations of Ideas and Notations, page 4) Variables In the notation, variables are ambiguous in denotation, preserve a recognizable identity appearing in various places in logical statements within a given context, and have a range of possible determination between any two variables which is the same or different. When the possible determination is the same for both variables, then one implies the other; otherwise, the possible determination of one given to the other produces a meaningless phrase. The alphabetic symbo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History One of the earliest known mathematicians were Thales of Miletus (c. 624–c.546 BC); he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. He is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales' Theorem. The number of known mathematicians grew when Pythagoras of Samos (c. 582–c. 507 BC) established the Pythagorean School, whose doctrine it was that mathematics ruled the universe and whose motto was "All is number". It was the Pythagoreans who coined the term "mathematics", and with whom the study of mathematics for its own sake begins. The first woman mathematician recorded by history was Hypati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Random House Webster's Unabridged Dictionary
''Random House Webster's Unabridged Dictionary'' is a large American dictionary, first published in 1966 as ''The Random House Dictionary of the English Language: The Unabridged Edition''. Edited by Editor-in-chief Jess Stein, it contained 315,000 entries in 2256 pages, as well as 2400 illustrations. The CD-ROM version in 1994 also included 120,000 spoken pronunciations. History The Random House publishing company entered the reference book market after World War II. They acquired rights to the ''Century Dictionary'' and the ''Dictionary of American English'', both out of print. Their first dictionary was Clarence Barnhart's ''American College Dictionary'', published in 1947, and based primarily on ''The New Century Dictionary'', an abridgment of the ''Century''. In the late 1950s, it was decided to publish an expansion of the ''American College Dictionary'', which had been modestly updated with each reprinting since its publication. Under editors Jess Stein and Laurence Ur ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Order Of The Crown Of Italy
The Order of the Crown of Italy ( it, Ordine della Corona d'Italia, italic=no or OCI) was founded as a national order in 1868 by King Vittorio Emanuele II, to commemorate the unification of Italy in 1861. It was awarded in five degrees for civilian and military merit. Today the Order of the Crown has been replaced by the Order of Merit of Savoy and is still conferred on new knights by the current head of the house of Vittorio Emanuele, Prince of Naples. Compared with the older Order of Saints Maurice and Lazarus (1572), the Order of the Crown of Italy was awarded more liberally and could be conferred on non-Catholics as well; eventually, it became a requirement for a person to have already received the Order of the Crown of Italy in at least the same degree before receiving the Order of Saints Maurice and Lazarus. The order has been suppressed by law since the foundation of the Republic in 1946. However, Umberto II did not abdicate his position as ''fons honorum'' and it rema ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Order Of Saints Maurizio And Lazzaro
The Order of Saints Maurice and Lazarus ( it, Ordine dei Santi Maurizio e Lazzaro) (abbreviated OSSML) is a Roman Catholic dynastic order of knighthood bestowed by the royal House of Savoy. It is the second-oldest order of knighthood in the world, tracing its lineage to AD 1098, and it is one of the rare orders of knighthood recognized by papal bull, in this case by Pope Gregory XIII. In that bull, Pope Gregory XIII bestowed upon Emmanuel Philibert, Duke of Savoy and his Savoy successors, the right to confer this knighthood in perpetuity. The Grand Master is, Vittorio Emanuele, Prince of Naples, also known as the Duke of Savoy, the eldest son of the last King of Italy, Umberto II of Italy. However Vittorio Emanuele's cousin once removed Prince Aimone, Duke of Aosta claims to be grand master as his father claimed to be head of the house of Savoy. The order was formerly awarded by the Kingdom of Italy (1861–1946) with the heads of the House of Savoy as the Kings of Italy. O ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Giovanni Vailati
Giovanni Vailati (24 April 1863 – 14 May 1909) was an Italian proto-analytic philosopher, historian of science, and mathematician. Life Vailati was born in Crema, Lombardy, and studied engineering at the University of Turin. He went on to lecture in the history of mechanics there from 1896 to 1899, after working as assistant to Giuseppe Peano and Vito Volterra. He resigned his university post in 1899 so that he could pursue his independent studies, making a living from high-school mathematics teaching. During his lifetime he became internationally known, his writings having been translated into English, French, and Polish, though he was largely forgotten after his death in Rome. He was rediscovered in the late 1950s. He did not publish any complete books, but left about 200 essays and reviews across a range of academic disciplines. Philosophy Vailati's view of philosophy was that it provided a preparation and the tools for scientific work. For that reason, and because phil ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bertrand Russell
Bertrand Arthur William Russell, 3rd Earl Russell, (18 May 1872 – 2 February 1970) was a British mathematician, philosopher, logician, and public intellectual. He had a considerable influence on mathematics, logic, set theory, linguistics, artificial intelligence, cognitive science, computer science and various areas of analytic philosophy, especially philosophy of mathematics, philosophy of language, epistemology, and metaphysics.Stanford Encyclopedia of Philosophy"Bertrand Russell" 1 May 2003. He was one of the early 20th century's most prominent logicians, and a founder of analytic philosophy, along with his predecessor Gottlob Frege, his friend and colleague G. E. Moore and his student and protégé Ludwig Wittgenstein. Russell with Moore led the British "revolt against idealism". Together with his former teacher A. N. Whitehead, Russell wrote ''Principia Mathematica'', a milestone in the development of classical logic, and a major attempt to reduce the whole ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gottlob Frege
Friedrich Ludwig Gottlob Frege (; ; 8 November 1848 – 26 July 1925) was a German philosopher, logician, and mathematician. He was a mathematics professor at the University of Jena, and is understood by many to be the father of analytic philosophy, concentrating on the philosophy of language, logic, and mathematics. Though he was largely ignored during his lifetime, Giuseppe Peano (1858–1932), Bertrand Russell (1872–1970), and, to some extent, Ludwig Wittgenstein (1889–1951) introduced his work to later generations of philosophers. Frege is widely considered to be the greatest logician since Aristotle, and one of the most profound philosophers of mathematics ever. His contributions include the development of modern logic in the ''Begriffsschrift'' and work in the foundations of mathematics. His book the ''Foundations of Arithmetic'' is the seminal text of the logicist project, and is cited by Michael Dummett as where to pinpoint the linguistic turn. His philosophical ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Angelo Genocchi
Angelo Genocchi (5 March 1817 – 7 March 1889) was an Italian mathematician who specialized in number theory. He worked with Giuseppe Peano. The Genocchi number In mathematics, the Genocchi numbers G''n'', named after Angelo Genocchi, are a sequence of integers that satisfy the relation : \frac=\sum_^\infty G_n\frac The first few Genocchi numbers are 0, −1, −1, 0, 1, 0, −3, 0, 17 , se ...s are named after him. Genocchi was President of the Academy of Sciences of Turin. Notes References * Obituary in: * 19th-century Italian mathematicians 1817 births 1889 deaths {{Italy-mathematician-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Euclid
Euclid (; grc-gre, Wikt:Εὐκλείδης, Εὐκλείδης; BC) was an ancient Greek mathematician active as a geometer and logician. Considered the "father of geometry", he is chiefly known for the ''Euclid's Elements, Elements'' treatise, which established the foundations of geometry that largely dominated the field until the early 19th century. His system, now referred to as Euclidean geometry, involved new innovations in combination with a synthesis of theories from earlier Greek mathematicians, including Eudoxus of Cnidus, Hippocrates of Chios, Thales and Theaetetus (mathematician), Theaetetus. With Archimedes and Apollonius of Perga, Euclid is generally considered among the greatest mathematicians of antiquity, and one of the most influential in the history of mathematics. Very little is known of Euclid's life, and most information comes from the philosophers Proclus and Pappus of Alexandria many centuries later. Until the early Renaissance he was often mistaken f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logicism
In the philosophy of mathematics, logicism is a programme comprising one or more of the theses that — for some coherent meaning of 'logic' — mathematics is an extension of logic, some or all of mathematics is reducible to logic, or some or all of mathematics may be modelled in logic. Bertrand Russell and Alfred North Whitehead championed this programme, initiated by Gottlob Frege and subsequently developed by Richard Dedekind and Giuseppe Peano. Overview Dedekind's path to logicism had a turning point when he was able to construct a model satisfying the axioms characterizing the real numbers using certain sets of rational numbers. This and related ideas convinced him that arithmetic, algebra and analysis were reducible to the natural numbers plus a "logic" of classes. Furthermore by 1872 he had concluded that the naturals themselves were reducible to sets and mappings. It is likely that other logicists, most importantly Frege, were also guided by the new theories of the real ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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