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.

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

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 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 ).

The concept goes back to Georg Cantor, who defined the notion of cardinality and realized that infinite sets can have different cardinalities.

" Meanwhile, back in New York City, Cantor Rabinovich confronts Rivka about Jess going to California and reminds her that her place is by her husband's side.

Cantor established the importance of one-to-one correspondence between the members of two sets, defined infinite and well-ordered sets, and proved that the real numbers are " more numerous " than the natural numbers.

In 1882, the mathematical correspondence between Cantor and Dedekind came to an end, apparently as a result of Dedekind's declining the chair at Halle.

Norman F. Cantor notes the three roles Boniface played that made him " one of the truly outstanding creators of the first Europe, as the apostle of Germany, the reformer of the Frankish church, and the chief fomentor of the alliance between the papacy and the Carolingian family.

In set theory, the Cantor – Bernstein – Schroeder theorem, named after Georg Cantor, Felix Bernstein, and Ernst Schröder, states that, if there exist injective functions and between the sets A and B, then there exists a bijective function.

Eddie Cantor is broadcast from NBC's Manhattan station WNBT to Philco's Philadelphia station WPTZ, via an automatic relay tower halfway between the two cities.

The Cantor function challenges naive intuitions about continuity and measure ; though it is continuous everywhere and has zero derivative almost everywhere, c goes from 0 to 1 as x goes from 0 to 1, and takes on every value in between.

In addition, he edited one of the most influential compilations of American historical documents, Documents of American History, which went through ten editions between 1938 and 1988 ( the tenth, and last, coedited with Commager's former student Milton Cantor.

He may have been a " Walter Cantor " at Ely Cathedral between 1443 and 1466, and he may have been the Walter Frye who joined the London Parish Clerks in 1456 ; he also may have been the Walter Frye who left a will at Canterbury in 1474.

A similar relationship between the projective hierarchy and the relativized analytical hierarchy holds for subsets of Cantor space and, more generally, subsets of any effective Polish space.

Cantor defined cardinality in terms of bijective functions: two sets have the same cardinality if and only if there exists a bijective function between them.

One of the greatest achievements of Georg Cantor was the construction of a one-to-one correspondence between the points of a square and the points of one of its edges by means of continued fractions.

In his book Gilligan Unbound, American literary critic Paul Cantor described how " Thirty Minutes Over Tokyo " references and mocks several aspects of Japanese and American culture, as well as differences between the two.

According to Cantor, this is where the family find a difference between Japanese and American culture, as Wink, the game-show host, explains to them: " Our game shows are a little different from yours.

This paradox is named for Georg Cantor, who is often credited with first identifying it in 1899 ( or between 1895 and 1897 ).

Earlier live action films to use the new Technicolor process include the final musical number in the feature The Cat and the Fiddle released by MGM in February 1934, and in short sequences filmed for other movies made during 1934, including The House of Rothschild ( 20th Century Pictures / United Artists ) with George Arliss and Kid Millions ( Samuel Goldwyn / United Artists ) with Eddie Cantor.

The Hollywood Stock Exchange, a virtual market game established in 1996 and now a division of Cantor Fitzgerald, LP, in which players buy and sell prediction shares of movies, actors, directors, and film-related options, correctly predicted 32 of 2006's 39 big-category Oscar nominees and 7 out of 8 top category winners.

Many of the famous comic performers of vaudeville, radio and movies came from the same place and the same era, including Gallagher and Shean, George Burns, Eddie Cantor, George Jessel and The Marx Brothers.