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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 created 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, while 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, gr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cuneo
Cuneo (; ; ; ) is a city and in Piedmont, 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 di Demonte, Stura and Gesso (river), Gesso. Cuneo is bounded by the municipalities of Beinette, Borgo San Dalmazzo, Boves, Piedmont, Boves, Busca, Piedmont, 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 – Traforo stradale del Colle di Tenda, Tunnel of Tenda at , long *Colle del Melogno at *Colle San Bernardo at *Colle di Nava at *Bocchetta di Altare, 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 marquisate of Monferrat, marquisses of Mo ... [...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 symb ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Notation
Mathematical notation consists of using glossary of mathematical symbols, symbols for representing operation (mathematics), operations, unspecified numbers, relation (mathematics), relations, and any other mathematical objects and assembling them into expression (mathematics), expressions and formulas. Mathematical notation is widely used in mathematics, science, and engineering for representing complex concepts and property (philosophy), properties in a concise, unambiguous, and accurate way. For example, the physicist Albert Einstein's formula E=mc^2 is the quantitative representation in mathematical notation of mass–energy equivalence. Mathematical notation was first introduced by François Viète at the end of the 16th century and largely expanded during the 17th and 18th centuries by René Descartes, Isaac Newton, Gottfried Wilhelm Leibniz, and overall Leonhard Euler. Symbols and typeface The use of many symbols is the basis of mathematical notation. They play a s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Set Theory
Set theory is the branch of mathematical logic that studies Set (mathematics), 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 of set theory, 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 the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Logic
Mathematical logic is the study of Logic#Formal logic, formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory (also known as computability theory). Research in mathematical logic commonly addresses the mathematical properties of formal systems of logic such as their expressive or deductive power. However, it can also include uses of logic to characterize correct mathematical reasoning or to establish foundations of mathematics. Since its inception, mathematical logic has both contributed to and been motivated by the study of foundations of mathematics. This study began in the late 19th century with the development of axiomatic frameworks for geometry, arithmetic, and Mathematical analysis, analysis. In the early 20th century it was shaped by David Hilbert's Hilbert's program, program to prove the consistency of foundational theories. Results of Kurt Gödel, Gerhard Gentzen, and others provided partial resolution to th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Glottologist
Historical linguistics, also known as diachronic linguistics, is the scientific study of how languages change over time. It seeks to understand the nature and causes of linguistic change and to trace the evolution of languages. Historical linguistics involves several key areas of study, including the reconstruction of ancestral languages, the classification of languages into families, (comparative linguistics) and the analysis of the cultural and social influences on language development. This field is grounded in the uniformitarian principle, which posits that the processes of language change observed today were also at work in the past, unless there is clear evidence to suggest otherwise. Historical linguists aim to describe and explain changes in individual languages, explore the history of speech communities, and study the origins and meanings of words (etymology). Development Modern historical linguistics dates to the late 18th century, having originally grown out ... [...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, mathematical structure, structure, space, Mathematical model, models, and mathematics#Calculus and analysis, change. History One of the earliest known mathematicians was Thales of Miletus (); 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's theorem. The number of known mathematicians grew when Pythagoras of Samos () 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 math ... [...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 Urdan ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Order Of The Crown Of Italy
The Order of the Crown of Italy ( or OCI) was founded as a national order in 1868 by King Victor Emmanuel II of Italy, Vittorio Emanuele II, to commemorate Italian unification, 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 Emanuele Filiberto, Prince of Venice. The order has been suppressed by law since the birth of the Italian Republic, foundation of the Republic in 1946. However, Umberto II of Italy, Umberto II did not abdicate his position as ''fons honorum'' and it remained under his Grand Mastership as a dynastic order. While the continued use of those decorations conferred prior to 1951 is permitted in Italy, the crowns on the ribbons issued before 1946 must be substituted for as many five pointed stars on military uniforms. Grades The various degrees of the order, with c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Order Of Saints Maurizio And Lazzaro
The Order of Saints Maurice and Lazarus () (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 Prince Emanuele Filiberto of Savoy, Prince of Venice, also known as the Duke of Savoy, the grandson of the last King of Italy, Umberto II. However, Emanuele Filiberto's cousin twice removed Prince Aimone, Duke of Aosta in theory claims to be the rightful 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. Origina ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Maria Gramegna
Maria Paola Gramegna (1887–1915) was an Italian mathematician and a student of Giuseppe Peano. Her work with Peano on systems of linear differential equations has been cited as an important early milestone in the history of functional analysis and its transition from working with concrete matrices to more abstract basis-independent formulations of linear algebra. After becoming a schoolteacher, she died in the 1915 Avezzano earthquake. Early life and education Gramegna was born on 11 May 1887 in Tortona, the youngest of five children of a pasta factory owner. After studying mathematics in high school in Voghera with Giuseppe Vitali, she was admitted to the University of Turin in 1906, where she became a student of Peano. She completed her mathematics degree in 1910, with the thesis ''Serie di equazioni differenziali lineari ed equazioni integro-differenziali'' 'Series of linear differential equations and integro-differential equations'' supervised by Peano. Peano also presented ... [...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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
