Cantor also mentioned the idea in his letters to Richard Dedekind ( text in square brackets not present in original ):

However, the term naive set theory is also used in some literature to refer to the set theories studied by Frege and Cantor, rather than to the informal counterparts of modern axiomatic set theory ; care is required to tell which sense is intended.

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.

Between 1870 and 1872, Cantor published more papers on trigonometric series, and also a paper defining irrational numbers as convergent sequences of rational numbers.

Cantor also published an erroneous " proof " of the inconsistency of infinitesimals.

Several hit songs were also recorded during the mahjong fad, most notably " Since Ma is Playing Mah Jong " by Eddie Cantor.

The Stanford trustees also oversee the Stanford Research Park, the Stanford Shopping Center, the Cantor Center for Visual Arts, Stanford University Medical Center, and many associated medical facilities ( including the Lucile Packard Children's Hospital ).

In the foundations of mathematics, Russell's paradox ( also known as Russell's antinomy ), discovered by Bertrand Russell in 1901, showed that the naive set theory created by Georg Cantor leads to a contradiction.

Cantor's diagonal argument, also called the diagonalisation argument, the diagonal slash argument or the diagonal method, was published in 1891 by Georg Cantor as a mathematical proof that there are infinite sets which cannot be put into one-to-one correspondence with the infinite set of natural numbers.

A standard example of a singular function is the Cantor function, which is sometimes called the devil's staircase ( a term also used for singular functions in general ).

The song also was featured in the movie The Eddie Cantor Story and was the theme of the television series of the same name in 1961 – 1962.

Cantor also recorded ODJB's " Palesteena ( Lena from Palesteena )".

That same year she also appeared on screen with Eddie Cantor in Kid Millions, but it was her return to Broadway that would establish her as a major star and cement her image as a tough girl with a soft heart.

See also: Cantor in Reform Judaism.

" 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.

The theorem is also known as the Schroeder – Bernstein theorem, the Cantor – Bernstein theorem, or the Cantor – Schroeder – Bernstein theorem.

She also wrote and directed an episode of Women for Showtime Cable Network, as well as Sax Cantor Riff, one of HBO ’ s Subway Stories for producers Jonathan Demme and Rosie Perez.

Note that we can also define the arithmetic hierarchy of subsets of the Cantor and Baire spaces relative to some set of integers.

Cantor also discovered and helped guide the career of singer Dinah Shore, first featuring her on his radio show in 1940, as well as other performers, including Deanna Durbin, Bobby Breen and Eddie Fisher.

Cantor was also a composer, with his most famous song seldom attributed to him.

Cantor also bounced back between movies and on radio.

Cantor also turned the role down ( so it went to Al Jolson ), but he became a leading Hollywood star in 1930 with the film version of Whoopee !, shot in two-color Technicolor.

On May 25, 1944, pioneer television station WPTZ ( now KYW-TV ) in Philadelphia presented a special telecast featuring Eddie Cantor, which was also fed to the NBC television station in New York City, WNBT ( now WNBC ).

Such sets are now known as uncountable sets, and the size of infinite sets is now treated by the theory of cardinal numbers which Cantor began.

By his early teens Cantor began winning talent contests at local theaters and started appearing on stage.

Cantor began making phonograph records in 1917, recording both comedy songs and routines and popular songs of the day, first for Victor, then for Aeoleon-Vocalion, Pathé and Emerson.

His earliest movie jobs were on Samuel Goldwyn's Eddie Cantor musicals, where he began developing such techniques as a “ parade of faces ” ( individualizing each chorus girl with a loving close-up ), and moving his dancers all over the stage ( and often beyond ) in as many kaleidoscopic patterns as possible.

Gilbert moved to Hollywood in 1915, and began writing for film, television, and radio ( including the Eddie Cantor show ).

Founded in the 2007 – 2008 election cycle by Congressmen Eric Cantor, Kevin McCarthy and Paul Ryan, the Young Guns Program began as an organization of House Republicans dedicated to electing open seat and challenger candidates nationwide.

Lilyan Tashman's entertainment career began in vaudeville, and by 1914 she was an experienced performer, appearing in Song Revue in Milwaukee, Wisconsin with rising stars Eddie Cantor and Al Lee.

Among Franklin's own idols, as he frequently told viewers, were Al Jolson, whom he literally " followed around " as a teenager in New York, and Eddie Cantor, who eventually began buying jokes from the young Franklin and whose Carnegie Hall show Franklin later produced.

Given a trigonometric series f ( x ) with S as its set of zeros, Cantor had discovered a procedure that produced another trigonometric series that had S ' as its set of zeros, where S ' is the set of limit points of S. If p ( 1 ) is the set of limit points of S, then he could construct a trigonometric series whose zeros are p ( 1 ).

The carpet is a generalization of the Cantor set to two dimensions ( another is Cantor dust ).

" On October 10, 1964 in Beverly Hills, California, Eddie Cantor suffered another heart attack and died, aged 72.

He came from a family that had emigrated to the Netherlands from Portugal, another branch of which had established itself in Russia, where Georg Cantor was born.

The Hénon attractor is a fractal, smooth in one direction and a Cantor set in another.

Cantor compared Kantorowicz with another contemporary German medievalist, Percy Ernst Schramm, who worked on similar topics and was a member of the Nazi Party.

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

Cantor developed important concepts in topology and their relation to cardinality.

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.