The axiom of choice was formulated in 1904 by Ernst Zermelo in order to formalize his proof of the well-ordering theorem.

Among the students of Hilbert were: Hermann Weyl, chess champion Emanuel Lasker, Ernst Zermelo, and Carl Gustav Hempel.

Although Ernst Zermelo demonstrated less than a day later that König's proof had failed, Cantor remained shaken, even momentarily questioning God.

Ernst Zermelo introduced the Axiom of Choice as an " unobjectionable logical principle " to prove the well-ordering theorem.

After reading Gibbs's textbook ( which was translated into German by Ernst Zermelo in 1905 ), Einstein declared that Gibbs's treatment was superior to his own and explained that he would not have written those papers if he had known Gibbs's work.

The same paradox had been discovered a year before by Ernst Zermelo but he did not publish the idea, which remained known only to Hilbert, Husserl and other members of the University of Göttingen.

In 1908, Ernst Zermelo proposed an axiomatization of set theory that avoided the paradoxes of naive set theory by replacing arbitrary set comprehension with weaker existence axioms, such as his axiom of separation ( Aussonderung ).

For his part, Ernst Zermelo in his ( 1908 ) A new proof of the possibility of a well-ordering ( published at the same time he published " the first axiomatic set theory ") laid claim to prior discovery of the antinomy in Cantor's naive set theory.

Ernst Zermelo was one of the major advocates of such a view ; he also developed much of axiomatic set theory.

In mathematics, Zermelo – Fraenkel set theory with the axiom of choice, named after mathematicians Ernst Zermelo and Abraham Fraenkel and commonly abbreviated ZFC, is one of several axiomatic systems that were proposed in the early twentieth century to formulate a theory of sets without the paradoxes of naive set theory such as Russell's paradox.

Ernst Friedrich Ferdinand Zermelo (; 1871 – 1953 )

# redirect Ernst Zermelo

Zermelo set theory, as set out in an important paper in 1908 by Ernst Zermelo, is the ancestor of modern set theory.

* Ernst Zermelo formulates the axiom of choice.

* Ernst Zermelo axiomizes set theory, thus avoiding Cantor's contradictions.

* Ernst Zermelo

He is known for his contributions to axiomatic set theory, especially his addition to Ernst Zermelo's axioms which resulted in Zermelo – Fraenkel axioms.

# REDIRECT Ernst Zermelo

An error in Kőnig's proof was discovered by Ernst Zermelo soon thereafter.

Of a totally different orientation < nowiki > the " Old Formalist School " of Richard Dedekind | Dedekind, Georg Cantor | Cantor, Giuseppe Peano | Peano, Ernst Zermelo | Zermelo, and Louis Couturat | Couturat, etc .< nowiki ></ nowiki > was the Pre-Intuitionist School, mainly led by Poincaré, Borel and Lebesgue.

Skolem's work was harshly received by Ernst Zermelo, who argued against the limitations of first-order logic, but the result quickly came to be accepted by the mathematical community.

Ernst Zermelo, the later editor of Cantor's collected works, found the error already the next day.

* 1908: Ernst Brenner

* 1907 – 1908: " Hohenhof ", Mansion for Karl Ernst Osthaus in Hagen, Germany

* Ernst I, Duke of Saxe-Altenburg ( 1853 – 1908 )

* Ernst II, Duke of Saxe-Altenburg ( 1908 – 1918 )

* Ernst König ( 1908 – 1986 ), Wehrmacht officer during World War II

In mathematics, the Phragmén – Lindelöf principle is a 1908 extension by Lars Edvard Phragmén ( 1863 – 1937 ) and Ernst Leonard Lindelöf of the maximum modulus principle of complex analysis, to unbounded domains.

Traugott Schiess, " Briefwechsel der Brüder Ambrosius und Thomas Blaurer 1509-1567 ", Freiburg: Ernst Fehsenfeld, 1908

* Ernst Kremnitz ( 1859 – 1908 ), German entrepreneur

Last Saturday's interesting melange included Ernst Toch, Karlheinz Stockhausen, Richard Yardumian and a brief excerpt from a new `` space '' opera by the Swedish composer, Karl-Birger Blomdahl.

Ernst Mayr approached the problem with a new definition for the concept of species.

The most important of the new film producers at the time was Joe May, who made a series of thrillers and adventure films through the war years, but Ernst Lubitsch also came into prominence with a series of very successful comedies and dramas.

Managing Director Ernst Fuhrmann was also pressuring Ferdinand to approve development of the new model in light of concerns that the current flagship model at the time, the 911, was quickly reaching its maximum potential where it could soon no longer be improved upon.

Heydrich's replacements were Ernst Kaltenbrunner as the chief of RSHA, and Karl Hermann Frank ( 27 – 28 May 1942 ) and Kurt Daluege ( 28 May 1942 – 14 October 1943 ) as the new acting Reichsprotektors.

The mass housing projects of Ernst May and Bruno Taut are evidence of markedly creative designs being incorporated as a major feature of new planned communities.

In 1996 Ernst and Jan H. accepted an offer to join Boudewijn de Groot's new touring band.

Ernst was still the left-engaged ladies man but even his lyrics explored new territories ; in Het Beste he decides that his fatherhood has become a failure, and in Overspel the ladies man has grown up to discover his potential for adultery ( although not succumbing to it ).

While the old term for electrical conductance, the mho ( the inverse of the resistance unit ohm ), is still used, a new name, the siemens, was adopted in 1971, honoring Ernst Werner von Siemens.

A social housing project in Frankfurt ( the Römerstadt of architect Ernst May ) realized in 1927 / 8 was the breakthrough for her Frankfurt kitchen, which embodied this new notion of efficiency in the kitchen.

The town has the enormous new Orthodox Cathedral Church of the Trinity, a recently completed Roman Catholic Church of the Nativity and the Mask of Sorrow memorial, a huge sculpture in memory of Stalin's victims, designed by Ernst Neizvestny.

The U. S. Securities and Exchange Commission and members of the investment community began to raise concerns about potential conflicts of interest between the consulting and auditing work amongst the Big Five and in May 2000, EY was the first of the firms to formally and fully separate its consulting practices via a sale to the French IT services company Cap Gemini for $ 11 billion, largely in stock, creating the new company of Cap Gemini Ernst & Young, which was later renamed Capgemini.

The launch of the new " Swatch " brand watch in 1983, by the then ETA SA CEO Ernst Thomke and his young team of engineers, was marked by bold new styling and design.

Following the ideas of Ernst Mach, Skinner rejected Thorndike's mediating structures required by " satisfaction " and constructed a new conceptualization of behavior without any such references.

The new government formed of Protestant nobility and gentry gave Ernst von Mansfeld the command over all of its forces.

At Lake Forest he published the first part of his " Handbook of Psychology ( Senses and Intellect )" in which he directed the attention to the new experimental psychology of Ernst Heinrich Weber, Fechner and Wundt.

After Napoleon's defeat in 1814 and the Prussian occupation of Paris by General Ernst von Pfuel, the Quadriga was restored to Berlin and Victoria's wreath of oak leaves was supplemented with a new symbol of Prussian power, the Iron Cross.

* October 30 – Ernst Marboe is announced as the new administrator of the Vienna State Opera and Burg Theater, replacing Egon Hilbert.

Hannover made a fresh start with a new team of hungry youngsters, many of whom went on to play for the national team ( Gerald Asamoah, Sebastian Kehl, Fabian Ernst ) or impress in the Bundesliga.

Goebbels and some others believed that the forceful works of such artists as Emil Nolde, Ernst Barlach and Erich Heckel exemplified the Nordic spirit ; as Goebbels explained, " We National Socialists are not unmodern ; we are the carrier of a new modernity, not only in politics and in social matters, but also in art and intellectual matters.

Speaking of the charitable and philanthropic institutions of the 19th century industrial era, Ernst Troeltsch said, " their aim was a new spirit, not a new society.

Christian Ernst, Margrave of Brandenburg-Bayreuth, built a " new town " ( Neustadt ) for them.