Cantor developed an entire theory and arithmetic of infinite sets, called cardinals and ordinals, which extended the arithmetic of the natural numbers.

In this context, Jordan developed his theory of measure, Cantor developed what is now called naive set theory, and Baire proved the Baire category theorem.

Implicitly, this is the universe that Georg Cantor was using when he first developed modern naive set theory and cardinality in the 1870s and 1880s in applications to real analysis.

Paul Cantor, a literary critic and economic theorist, who has taught college courses revolving around the " Gnomes " episode, has described it as " the most fully developed defense of capitalism " ever produced by the show.

Based on his experience at Cantor Fitzgerald, Pulver developed a market where IP Telephony minutes and capacity could be traded in both spot and futures contracts.

Mistakes and philosophical weaknesses in reasoning about infinitesimal numbers in the work of Gottfried Leibniz, Johann Bernoulli, Leonhard Euler, Augustin-Louis Cauchy, and others were the reason that they were originally abandoned for the more cumbersome real number-based arguments developed by Georg Cantor, Richard Dedekind, and Karl Weierstrass, which were perceived as being more rigorous by Weierstrass's followers.

The concept was first introduced by Georg Cantor in 1872 and he developed set theory in large part to study derived sets on the real line.

In mathematical logic, the theory of infinite sets was first developed by Georg Cantor.

At Columbia University in 1984, Schwartz and Cantor developed a variation on the standard protocol by introducing an alternating voltage gradient to improve the resolution of larger molecules.

Cantor also began another important correspondence, with Gösta Mittag-Leffler in Sweden, and soon began to publish in Mittag-Leffler's journal Acta Mathematica.

Cantor recovered soon thereafter, and subsequently made further important contributions, including his famous diagonal argument and theorem.

His collection of American art was strong in Abstract expressionism, Pop Art, Minimalism, Neo-Dada, Color Field, Lyrical Abstraction, and Neo-Expressionism and he often donated important works from his collection to institutions like MoMA, and other important private museums and University collections like the Norton Simon Museum, the Sheldon Museum of Art and the Iris & B. Gerald Cantor Center for Visual Arts at Stanford University among many others.

An important example of a totally disconnected space is the Cantor set.

Two important members of the Notre Dame administration have been suggested as possible identities for Perotinus: the theologian Petrus Cantor ( who died in 1197 ) and the Petrus who was Succentor of Notre Dame from at least 1207 until about 1238.

Norman Cantor recognized three books as most important to Strayer's legacy: Feudalism ( 1965 ), which summarized three decades of his research and thinking on the topic ; On the Medieval Origins of the Modern State ( 1970 ), in which he shows the relevance of medieval historical institutions to modern governmental institutions ; and The Reign of Philip the Fair ( 1980 ), representing over 30 years of archival research and the most comprehensive work on the topic in any language-other than Jean Favier's Philippe le Bel ( 1978 ).

Cantor says it is important for " its brilliant summary of European political history from about 1050 to 1350 ".

The choice of the Polish space in the third clause above is not very important ; it could be replaced in the definition by a fixed uncountable Polish space, say Baire space or Cantor space or the real line.

As with many other episodes in the series, " Thirty Minutes Over Tokyo " suggests that, in the end, the Simpsons are more attached to the local than to the global, and, as Cantor writes: " indeed the global is ultimately important in the series only insofar as it can be made local, that is, part of Springfield.

Bernoulli schemes are important in the study of dynamical systems, as most such systems ( such as Axiom A systems ) exhibit a repellor that is the product of the Cantor set and a smooth manifold, and the dynamics on the Cantor set are isomorphic to that of the Bernoulli shift.

Through consideration of it, Cantor and others helped lay the foundations of modern general topology.

* Every subset of Baire space or Cantor space is an open set in the usual topology on the space.

* The Cantor set is a Baire space, and so is of second category in itself, but it is of first category in the interval 1 with the usual topology.

In topology and related areas of mathematics a uniformly connected space or Cantor connected space is a uniform space U such that every uniformly continuous function from U to a discrete uniform space is constant.

More abstractly, a natural class of objects to study in topology are objects that are homogeneous ( all points are topologically the same: the group of self-homeomorphisms acts transitively ) and " finite type " or " tame " ( to rule out spaces such as the Cantor set, where each open set contains uncountably many connected components ); more generally, a space of " finite type " where the self-homeomorphism group has finitely many orbits, forming the strata.

The US philosopher Charles Sanders Peirce praised Cantor's set theory, and, following public lectures delivered by Cantor at the first International Congress of Mathematicians, held in Zurich in 1897, Hurwitz and Hadamard also both expressed their admiration.

In spring 1899 Braun, accompanied by his colleagues Cantor and Zenneck, went to Cuxhaven to continue their experiments at the North Sea.

Historian Norman Cantor who specialized in the medieval period, teaching and writing at Columbia and New York University, says in 1993: " It may be true that the Arabs had now fully extended their resources and they would not have conquered France, but their defeat ( at Tours ) in 732 put a stop to their advance to the north.

In 1951 the duo became one of the rotating hosts of The Colgate Comedy Hour ( Eddie Cantor and Bob Hope were among the others ) and the following year they inaugurated their own situation comedy, The Abbott and Costello Show.

" Shakespeare scholar Paul A. Cantor argues that this association is appropriate — the warlike Klingons find their literary matches in the characters Othello, Mark Antony, and Macbeth — but that it also reinforces a claim that the end of the Cold War means the end of heroic literature such as Shakespeare's.

Dedekind, Riemann, Moritz Cantor and Alfred Enneper, although they had all already earned their PhDs, attended Dirichlet's classes to study with him.

Eddie Cantor is one of the four " down on their luck " stars ( along with Bing Crosby, Al Jolson and Jack Benny ) snubbed by Elmer Fudd in What ’ s Up, Doc?

With the full set, companies could mail a single Cantor card each month for a year to their selected special customers as an ongoing promotion.

Many fields of mathematics bear the imprint of their creators for notation: the differential operator is due to Leibniz, the cardinal infinities to Georg Cantor ( in addition to the lemniscate (∞) of John Wallis ), the congruence symbol (≡) to Gauss, and so forth.

Cantor said the episode challenges the stereotype that small businesses are public servants who truly care about their customers by portraying local business owner Mr. Tweek as greedier and having fewer scruples than that of the corporation he is challenging ; Tweek knowingly takes advantage of American distrust for big businesses and nostalgia for simpler times in his fight to maintain his bottom line.

Cantor has said the fact that the gnomes themselves do not understand their own business plan or why they steal the underwear could represent the idea that businessmen themselves often lack the economic knowledge needed to explain their activity and profits to the public.

Comics who appeared in burlesque early in their careers included Fanny Brice, Mae West, Eddie Cantor, Abbott and Costello, W. C. Fields, Jackie Gleason, Danny Thomas, Al Jolson, Bert Lahr, Phil Silvers, Sid Caesar, Danny Kaye, Red Skelton and Sophie Tucker.

Galea left the Freestylers shortly after the release of the Freestyle EP, and Cantor and Harvey formed an 11-piece band ( initially an idea of their record label, Freskanova ).

In 1999 Strassen was awarded the Cantor medal, and in 2003 he was co-recipient of the Paris Kanellakis Award with Robert Solovay, Gary Miller, and Michael Rabin for their work on randomized primality testing.

Norman F. Cantor often highlighted his status as a student of Strayer's, but several of Strayer's other pupils-who wish to remain anonymous for personal and professional reasons-have expressed their doubt that Strayer ever acknowledged Cantor as his student or that Cantor had any formal affiliation with him at all.

Cantor describes Southern in Arthurian terms, with a group of devotees who surrounded their master following the publication of The Making of the Middle Ages.

Some casinos use third-party operators for their sportsbooks, such as Cantor Gaming, Leroy's, Lucky's, and Club Cal Neva.