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Mahlo Cardinals
Friedrich Paul Mahlo (born 28 July 1883 in Coswig, Anhalt; died 20 August 1971 in Halle, Saxony-Anhalt) was a German mathematician. Mahlo introduced Mahlo cardinals in 1911. He also showed that the continuum hypothesis implies the existence of a Luzin set In mathematics, a Luzin space (or Lusin space), named for N. N. Luzin, is an uncountable topological T1 space without isolated points in which every nowhere-dense subset is countable. There are many minor variations of this definition in use: t .... Publications * PhD dissertation * * References Further reading * {{DEFAULTSORT:Mahlo, Paul 20th-century German mathematicians Set theorists 1883 births 1971 deaths ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Coswig, Anhalt
Coswig is a town in the district of Wittenberg of Saxony-Anhalt, Germany. It is situated on the right bank of the Elbe, approx. 12 km west of Wittenberg, and 15 km east of Dessau. History The Castle of Coswig was mentioned first in 1187. There is no evidence for slav settlements before this date. In 1215 Coswig is called an "Oppidium". During this time it was one of the most important cities North of the river Elbe. In the 16th century Coswig was already connected to a drinking water pipe from Wörpen. Weaving, pottery and farming played the most important role in economics. The city was nearly completely destroyed by Hispanic troops during the Schmalkaldic War. From 1603 to 1793, Coswig belonged to Anhalt-Zerbst. The Castle was constructed at the end of the 17th century. The railway station was inaugurated on 10 September 1841. In 1987 the city celebrated its 800th-year of existence. Geography The town Coswig consists of Coswig proper and the following ''Ortschaf ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Halle, Saxony-Anhalt
Halle (Saale), or simply Halle (; from the 15th to the 17th century: ''Hall in Sachsen''; until the beginning of the 20th century: ''Halle an der Saale'' ; from 1965 to 1995: ''Halle/Saale'') is the largest city of the German state of Saxony-Anhalt, the fifth most populous city in the area of former East Germany after (East) Berlin, Leipzig, Dresden and Chemnitz, as well as the 31st largest city of Germany, and with around 239,000 inhabitants, it is slightly more populous than the state capital of Magdeburg. Together with Leipzig, the largest city of Saxony, Halle forms the polycentric Leipzig-Halle conurbation. Between the two cities, in Schkeuditz, lies Leipzig/Halle International Airport. The Leipzig-Halle conurbation is at the heart of the larger Central German Metropolitan Region. Halle lies in the south of Saxony-Anhalt, in the Leipzig Bay, the southernmost part of the North German Plain, on the River Saale (a tributary of the Elbe), which is the third longest river flo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
German People
, native_name_lang = de , region1 = , pop1 = 72,650,269 , region2 = , pop2 = 534,000 , region3 = , pop3 = 157,000 3,322,405 , region4 = , pop4 = 21,000 3,000,000 , region5 = , pop5 = 125,000 982,226 , region6 = , pop6 = 900,000 , region7 = , pop7 = 142,000 840,000 , region8 = , pop8 = 9,000 500,000 , region9 = , pop9 = 357,000 , region10 = , pop10 = 310,000 , region11 = , pop11 = 36,000 250,000 , region12 = , pop12 = 25,000 200,000 , region13 = , pop13 = 233,000 , region14 = , pop14 = 211,000 , region15 = , pop15 = 203,000 , region16 = , pop16 = 201,000 , region17 = , pop17 = 101,000 148,00 ... [...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] |
Deutsche Mathematiker-Vereinigung
The German Mathematical Society (german: Deutsche Mathematiker-Vereinigung, DMV) is the main professional society of German mathematicians and represents German mathematics within the European Mathematical Society (EMS) and the International Mathematical Union (IMU). It was founded in 1890 in Bremen with the set theorist Georg Cantor as first president. Founding members included Georg Cantor, Felix Klein, Walther von Dyck, David Hilbert, Hermann Minkowski, Carl Runge, Rudolf Sturm, Hermann Schubert, and Heinrich Weber. The current president of the DMV is Ilka Agricola (2021–2022). Activities In honour of its founding president, Georg Cantor, the society awards the Cantor Medal. The DMV publishes two scientific journals, the ''Jahresbericht der DMV'' and ''Documenta Mathematica''. It also publishes a quarterly magazine for its membership the ''Mitteilungen der DMV''. The annual meeting of the DMV is called the ''Jahrestagung''; the DMV traditionally meets every four ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mahlo Cardinal
In mathematics, a Mahlo cardinal is a certain kind of large cardinal number. Mahlo cardinals were first described by . As with all large cardinals, none of these varieties of Mahlo cardinals can be proven to exist by ZFC (assuming ZFC is consistent). A cardinal number \kappa is called strongly Mahlo if \kappa is strongly inaccessible and the set U = \ is stationary in κ. A cardinal \kappa is called weakly Mahlo if \kappa is weakly inaccessible and the set of weakly inaccessible cardinals less than \kappa is stationary in \kappa. The term "Mahlo cardinal" now usually means "strongly Mahlo cardinal", though the cardinals originally considered by Mahlo were weakly Mahlo cardinals. Minimal condition sufficient for a Mahlo cardinal * If κ is a limit ''ordinal'' and the set of regular ordinals less than κ is stationary in κ, then κ is weakly Mahlo. The main difficulty in proving this is to show that κ is regular. We will suppose that it is not regular and construct a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Continuum Hypothesis
In mathematics, the continuum hypothesis (abbreviated CH) is a hypothesis about the possible sizes of infinite sets. It states that or equivalently, that In Zermelo–Fraenkel set theory with the axiom of choice (ZFC), this is equivalent to the following equation in aleph numbers: 2^=\aleph_1, or even shorter with beth numbers: \beth_1 = \aleph_1. The continuum hypothesis was advanced by Georg Cantor in 1878, and establishing its truth or falsehood is the first of Hilbert's 23 problems presented in 1900. The answer to this problem is independent of ZFC, so that either the continuum hypothesis or its negation can be added as an axiom to ZFC set theory, with the resulting theory being consistent if and only if ZFC is consistent. This independence was proved in 1963 by Paul Cohen, complementing earlier work by Kurt Gödel in 1940. The name of the hypothesis comes from the term '' the continuum'' for the real numbers. History Cantor believed the continuum hypothesis to be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Luzin Set
In mathematics, a Luzin space (or Lusin space), named for N. N. Luzin, is an uncountable topological T1 space without isolated points in which every nowhere-dense subset is countable. There are many minor variations of this definition in use: the T1 condition can be replaced by T2 or T3, and some authors allow a countable or even arbitrary number of isolated points. The existence of a Luzin space is independent of the axioms of ZFC. showed that the continuum hypothesis implies that a Luzin space exists. showed that assuming Martin's axiom and the negation of the continuum hypothesis, there are no Hausdorff Luzin spaces. In real analysis In real analysis and descriptive set theory, a Luzin set (or Lusin set), is defined as an uncountable subset of the reals such that every uncountable subset of is nonmeager; that is, of second Baire category. Equivalently, is an uncountable set of reals that meets every first category set in only countably many points. Luzin proved t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Set Theorists
Set, The Set, SET or SETS may refer to: Science, technology, and mathematics Mathematics *Set (mathematics), a collection of elements *Category of sets, the category whose objects and morphisms are sets and total functions, respectively Electronics and computing *Set (abstract data type), a data type in computer science that is a collection of unique values ** Set (C++), a set implementation in the C++ Standard Library * Set (command), a command for setting values of environment variables in Unix and Microsoft operating-systems * Secure Electronic Transaction, a standard protocol for securing credit card transactions over insecure networks * Single-electron transistor, a device to amplify currents in nanoelectronics * Single-ended triode, a type of electronic amplifier * Set!, a programming syntax in the scheme programming language Biology and psychology * Set (psychology), a set of expectations which shapes perception or thought *Set or sett, a badger's den *Set, a small tuber ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1883 Births
Events January–March * January 4 – ''Life'' magazine is founded in Los Angeles, California, United States. * January 10 – A fire at the Newhall Hotel in Milwaukee, Wisconsin, United States, kills 73 people. * January 16 – The Pendleton Civil Service Reform Act, establishing the United States civil service, is passed. * January 19 – The first electric lighting system employing overhead wires begins service in Roselle, New Jersey, United States, installed by Thomas Edison. * February – ''The Adventures of Pinocchio'' by Carlo Collodi is first published complete in book form, in Italy. * February 15 – Tokyo Electrical Lightning Grid, predecessor of Tokyo Electrical Power (TEPCO), one of the largest electrical grids in Asia and the world, is founded in Japan. * February 16 – The '' Ladies' Home Journal'' is published for the first time, in the United States. * February 23 – Alabama becomes the first U.S. stat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
