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Abraham Adolf Fraenkel
Abraham Fraenkel ( he, אברהם הלוי (אדולף) פרנקל; February 17, 1891 – October 15, 1965) was a German-born Israeli mathematician. He was an early Zionist and the first Dean of Mathematics at the Hebrew University of Jerusalem. He is known for his contributions to axiomatic set theory, especially his additions to Ernst Zermelo's axioms, which resulted in the Zermelo–Fraenkel set theory. Biography Abraham Adolf Halevi Fraenkel studied mathematics at the Universities of Munich, Berlin, Marburg and Breslau. After graduating, he lectured at the University of Marburg from 1916, and was promoted to professor in 1922. In 1919 he married Wilhelmina Malka A. Prins (1892–1983). Due to the severe housing shortage in post-war Germany, for a few years the couple lived as subtenants at professor Hensel's place. After leaving Marburg in 1928, Fraenkel taught at the University of Kiel for a year. He then made the fateful choice of accepting a position at the Hebrew Unive ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Munich
Munich ( ; german: München ; bar, Minga ) is the capital and most populous city of the States of Germany, German state of Bavaria. With a population of 1,558,395 inhabitants as of 31 July 2020, it is the List of cities in Germany by population, third-largest city in Germany, after Berlin and Hamburg, and thus the largest which does not constitute its own state, as well as the List of cities in the European Union by population within city limits, 11th-largest city in the European Union. The Munich Metropolitan Region, city's metropolitan region is home to 6 million people. Straddling the banks of the River Isar (a tributary of the Danube) north of the Northern Limestone Alps, Bavarian Alps, Munich is the seat of the Bavarian Regierungsbezirk, administrative region of Upper Bavaria, while being the population density, most densely populated municipality in Germany (4,500 people per km2). Munich is the second-largest city in the Bavarian dialects, Bavarian dialect area, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Professor
Professor (commonly abbreviated as Prof.) is an Academy, academic rank at university, universities and other post-secondary education and research institutions in most countries. Literally, ''professor'' derives from Latin as a "person who professes". Professors are usually experts in their field and teachers of the highest rank. In most systems of List of academic ranks, academic ranks, "professor" as an unqualified title refers only to the most senior academic position, sometimes informally known as "full professor". In some countries and institutions, the word "professor" is also used in titles of lower ranks such as associate professor and assistant professor; this is particularly the case in the United States, where the unqualified word is also used colloquially to refer to associate and assistant professors as well. This usage would be considered incorrect among other academic communities. However, the otherwise unqualified title "Professor" designated with a capital let ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting points of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Foundations Of Mathematics
Foundations of mathematics is the study of the philosophy, philosophical and logical and/or algorithmic basis of mathematics, or, in a broader sense, the mathematical investigation of what underlies the philosophical theories concerning the nature of mathematics. In this latter sense, the distinction between foundations of mathematics and philosophy of mathematics turns out to be quite vague. Foundations of mathematics can be conceived as the study of the basic mathematical concepts (set, function, geometrical figure, number, etc.) and how they form hierarchies of more complex structures and concepts, especially the fundamentally important structures that form the language of mathematics (formulas, theories and their model theory, models giving a meaning to formulas, definitions, proofs, algorithms, etc.) also called metamathematics, metamathematical concepts, with an eye to the philosophical aspects and the unity of mathematics. The search for foundations of mathematics is a cent ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 foundational ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Zermelo
Ernst Friedrich Ferdinand Zermelo (, ; 27 July 187121 May 1953) was a German logician and mathematician, whose work has major implications for the foundations of mathematics. He is known for his role in developing Zermelo–Fraenkel axiomatic set theory and his proof of the well-ordering theorem. Furthermore, his 1929 work on ranking chess players is the first description of a model for pairwise comparison that continues to have a profound impact on various applied fields utilizing this method. Life Ernst Zermelo graduated from Berlin's Luisenstädtisches Gymnasium (now ) in 1889. He then studied mathematics, physics and philosophy at the University of Berlin, the University of Halle, and the University of Freiburg. He finished his doctorate in 1894 at the University of Berlin, awarded for a dissertation on the calculus of variations (''Untersuchungen zur Variationsrechnung''). Zermelo remained at the University of Berlin, where he was appointed assistant to Planck, under whose ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ring (mathematics)
In mathematics, rings are algebraic structures that generalize fields: multiplication need not be commutative and multiplicative inverses need not exist. In other words, a ''ring'' is a set equipped with two binary operations satisfying properties analogous to those of addition and multiplication of integers. Ring elements may be numbers such as integers or complex numbers, but they may also be non-numerical objects such as polynomials, square matrices, functions, and power series. Formally, a ''ring'' is an abelian group whose operation is called ''addition'', with a second binary operation called ''multiplication'' that is associative, is distributive over the addition operation, and has a multiplicative identity element. (Some authors use the term " " with a missing i to refer to the more general structure that omits this last requirement; see .) Whether a ring is commutative (that is, whether the order in which two elements are multiplied might change the result) has ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ring Theory
In algebra, ring theory is the study of rings— algebraic structures in which addition and multiplication are defined and have similar properties to those operations defined for the integers. Ring theory studies the structure of rings, their representations, or, in different language, modules, special classes of rings (group rings, division rings, universal enveloping algebras), as well as an array of properties that proved to be of interest both within the theory itself and for its applications, such as homological algebra, homological properties and Polynomial identity ring, polynomial identities. Commutative rings are much better understood than noncommutative ones. Algebraic geometry and algebraic number theory, which provide many natural examples of commutative rings, have driven much of the development of commutative ring theory, which is now, under the name of ''commutative algebra'', a major area of modern mathematics. Because these three fields (algebraic geometry, alge ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
P-adic Number
In mathematics, the -adic number system for any prime number extends the ordinary arithmetic of the rational numbers in a different way from the extension of the rational number system to the real and complex number systems. The extension is achieved by an alternative interpretation of the concept of "closeness" or absolute value. In particular, two -adic numbers are considered to be close when their difference is divisible by a high power of : the higher the power, the closer they are. This property enables -adic numbers to encode congruence information in a way that turns out to have powerful applications in number theory – including, for example, in the famous proof of Fermat's Last Theorem by Andrew Wiles. These numbers were first described by Kurt Hensel in 1897, though, with hindsight, some of Ernst Kummer's earlier work can be interpreted as implicitly using -adic numbers.Translator's introductionpage 35 "Indeed, with hindsight it becomes apparent that a d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mizrachi (Religious Zionism)
The Mizrachi ( he, תנועת הַמִזְרָחִי, ''Tnuat HaMizrahi'') is a religious Zionist organization founded in 1902 in Vilnius at a world conference of religious Zionists called by Rabbi Yitzchak Yaacov Reines. Bnei Akiva, which was founded in 1929, is the youth movement associated with Mizrachi. Both Mizrachi and the Bnei Akiva youth movement continued to function as international movements. Here the word "Mizrahi" is a notarikon (a kind of acronym) for "Merkaz Ruhani" lit. ''Spiritual centre'': מרכז רוחני, introduced by rabbi Samuel Mohilever. Mizrachi believes that the Torah should be at the centre of Zionism and also sees Jewish nationalism as a means of achieving religious objectives. The Mizrachi Party was the first official religious Zionist party and founded the Ministry of Religious Affairs in Israel and pushed for laws enforcing kashrut and the observance of the sabbath in the workplace. It also played a role prior to the creation of the state of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mandatory Palestine
Mandatory Palestine ( ar, فلسطين الانتدابية '; he, פָּלֶשְׂתִּינָה (א״י) ', where "E.Y." indicates ''’Eretz Yiśrā’ēl'', the Land of Israel) was a geopolitical entity established between 1920 and 1948 in the region of Palestine under the terms of the League of Nations Mandate for Palestine. During the First World War (1914–1918), an Arab uprising against Ottoman rule and the British Empire's Egyptian Expeditionary Force under General Edmund Allenby drove the Ottoman Turks out of the Levant during the Sinai and Palestine Campaign. The United Kingdom had agreed in the McMahon–Hussein Correspondence that it would honour Arab independence if the Arabs revolted against the Ottoman Turks, but the two sides had different interpretations of this agreement, and in the end, the United Kingdom and France divided the area under the Sykes–Picot Agreementan act of betrayal in the eyes of the Arabs. Further complicating the issue was t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Assembly Of Representatives (Mandate Palestine)
The Assembly of Representatives ( he, אספת הנבחרים, ''Asefat HaNivharim'') was the elected parliamentary assembly of the Jewish community in Mandatory Palestine. It was established on 19 April 1920, and functioned until 13 February 1949, the day before the first Knesset, elected on 25 January, was sworn in. The Assembly met once a year to elect the executive body, the Jewish National Council, which was responsible for education, local government, welfare, security and defense. It also voted on the budgets proposed by the Jewish National Council and the Rabbinical Council. History Under the British Mandate, the Yishuv (Jewish community), established a network of political and administrative institutions, among them the Assembly of Representatives. To ensure that small groups were properly represented, a system of proportional representation was introduced. The first elections were held on 19 April 1920, and the largest faction, Ahdut HaAvoda, won only 70 of the Assembly' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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