Cantor was the first company to receive approval from the Nevada Gaming Commission to operate mobile gaming devices.

Cantor suffered his first known bout of depression in 1884.

In 1890, Cantor was instrumental in founding the Deutsche Mathematiker-Vereinigung and chaired its first meeting in Halle in 1891, where he first introduced his diagonal argument ; his reputation was strong enough, despite Kronecker's opposition to his work, to ensure he was elected as the first president of this society.

In one of his earliest papers, Cantor proved that the set of real numbers is " more numerous " than the set of natural numbers ; this showed, for the first time, that there exist infinite sets of different sizes.

The Continuum hypothesis, introduced by Cantor, was presented by David Hilbert as the first of his twenty-three open problems in his famous address at the 1900 International Congress of Mathematicians in Paris.

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.

Dedekind, whom Cantor befriended in 1872, cited this paper later that year, in the paper where he first set out his celebrated definition of real numbers by Dedekind cuts.

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.

Georg Cantor was the first to propose the question of whether is equal to.

The usage of the word abscissa is first recorded in 1659 by Stefano degli Angeli, a mathematics professor in Rome, according to Moritz Cantor.

He withdrew from public life in 747 to take up the monastic habit, " the first of a new type of saintly king ," according to Norman Cantor, " more interested in religious devotion than royal power, who frequently appeared in the following three centuries and who was an indication of the growing impact of Christian piety on Germanic society ".

In 2007, Stanford's Cantor Arts Center opened an exhibition, " Art of Being Tuareg: Sahara Nomads in a Modern World ", the first such exhibit in the United States.

* Eddie Cantor makes his first recordings

The species was first described by the Danish naturalist Theodore Edward Cantor in 1836.

* 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.

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 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.

Cantor, one of the first major stars to agree to appear on television, was to sing " We're Havin ' a Baby, My Baby and Me ".

Cantor and three of his daughters strike a pose in 1926 to promote his first film, Kid Boots, and children's shoes.

The first three, due to Georg Cantor / Charles Méray, Richard Dedekind and Karl Weierstrass / Otto Stolz all occurred within a few years of each other.

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.

When Al Flood became CEO, one of his first acts was to fire his chief rival Paul Cantor.

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.

By proving that there are ( infinitely ) many possible sizes for infinite sets, Cantor established that set theory was not trivial, and it needed to be studied.

Cantor established these results using two constructions.

The show established Cantor as a leading comedian, and his scriptwriter, David Freedman, as “ the Captain of Comedy .” Cantor soon became the world's highest-paid radio star.

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.

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.

* Hamadryas, the genus of the King Cobra invalidly established by Cantor in 1838 ; now Ophiophagus

For example, Georg Cantor ( who introduced this concept ) demonstrated that the real numbers cannot be put into one-to-one correspondence with the natural numbers ( non-negative integers ), and therefore that the set of real numbers has a greater cardinality than the set of natural numbers.

The notion of cardinality, as now understood, was formulated by Georg Cantor, the originator of set theory, in 1874 – 1884.

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

For example, he showed that the Cantor set is nowhere dense, but has the same cardinality as the set of all real numbers, whereas the rationals are everywhere dense, but countable.

While extending the notion of number by means of his revolutionary concept of infinite cardinality, Cantor was paradoxically opposed to theories of infinitesimals of his contemporaries Otto Stolz and Paul du Bois-Reymond, describing them as both " an abomination " and " a cholera bacillus of mathematics ".

In fact the cardinality of sets fails to be totally ordered ( see Cantor – Bernstein – Schroeder theorem ).

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

The oldest definition of the cardinality of a set X ( implicit in Cantor and explicit in Frege and Principia Mathematica ) is as the set of all sets which are equinumerous with X: this does not work in ZFC or other related systems of axiomatic set theory because this collection is too large to be a set, but it does work in type theory and in New Foundations and related systems.

) As Cantor realized, this collection could not itself have a cardinality, as this would lead to a paradox of the Burali-Forti type.

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.

Georg Cantor introduced the concept of cardinality to compare the sizes of infinite sets.

Before Cantor, there were only finite sets ( which are easy to understand ) and " the infinite " ( which was considered a topic for philosophical, rather than mathematical, discussion ).

A parallel definition is used to define the arithmetical hierarchy on finite Cartesian powers of Baire space or Cantor space, using formulas with several free variables.

The term transfinite was coined by Georg Cantor, who wished to avoid some of the implications of the word infinite in connection with these objects, which were nevertheless not finite.

In spite of this, there exists a homeomorphism of the cube having finite distortion that " squeezes the sponge " in the sense that the holes in the sponge go to a Cantor set of zero measure.

Note that, commonly, 2 < sup > ω </ sup > is referred to simply as the Cantor set, while the term Cantor space is reserved for the more general construction of D < sup > S </ sup > for a finite set D and a set S which might be finite, countable or possibly uncountable.

That is, in the Cantor normal form there is no finite number as last term, and the ordinal is nonzero.

Because Cantor space is homeomorphic to any finite Cartesian power of itself, and Baire space is homeomorphic to any finite Cartesian power of itself, the analytical hierarchy applies equally well to finite Cartesian power of one of these spaces.

However, some of these sets contain subclasses that are not sets, which makes them different from Cantor ( ZF ) finite sets and they are called infinite in AST.

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.