Cantor suffered his first known bout of depression in 1884.

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

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

David Hilbert defended it from its critics by famously declaring: " No one shall expel us from the Paradise that Cantor has created.

In 1860, Cantor graduated with distinction from the Realschule in Darmstadt ; his exceptional skills in mathematics, trigonometry in particular, were noted.

Cantor was able to support a family despite modest academic pay, thanks to his inheritance from his father.

He asked Cantor to withdraw the paper from Acta while it was in proof, writing that it was "... about one hundred years too soon.

Setting aside the animosity Kronecker had displayed towards him, Cantor invited him to address the meeting, but Kronecker was unable to do so because his wife was dying from injuries sustained in a skiing accident at the time.

Cantor retired in 1913, living in poverty and suffering from malnourishment during World War I.

One of the most vigorous and fruitful branches of mathematics [...] a paradise created by Cantor from which nobody shall ever expel us [...] the most admirable blossom of the mathematical mind and altogether one of the outstanding achievements of man's purely intellectual activity.

* Fractals derived from standard geometry by using iterative transformations on an initial common figure like a straight line ( the Cantor dust or the von Koch curve ), a triangle ( the Sierpinski triangle ), or a cube ( the Menger sponge ).

For one example ( a variant of the Cantor set ), remove from all dyadic fractions, i. e. fractions of the form a / 2 < sup > n </ sup > in lowest terms for positive integers a and n, and the intervals around them: ( a / 2 < sup > n </ sup > − 1 / 2 < sup > 2n + 1 </ sup >, a / 2 < sup > n </ sup > + 1 / 2 < sup > 2n + 1 </ sup >).

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

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.

* Audio Recording of Cantor Yossele Rosenblatt's Dew Service from the Florida Atlantic University Judaica Sound Archives ( Hebrew audio )

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 ".

When Cantor departed, Durante took over the NBC show as its star from April 22 to September 30, 1934, moving on to The Jumbo Fire Chief Program ( 1935 – 36 ).

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.

* SUBWAYStories: Tales from the Underground ( 1997 ) ( TV ) ( segment " Sax Cantor Riff ")

* SUBWAYStories: Tales from the Underground ( 1997 ) ( TV ) ( segment " Sax Cantor Riff ")

Note that elements of the Cantor space can be identified with sets of integers and elements of the Baire space with functions from integers to integers.

* A subset of Baire space has a corresponding subset of Cantor space under the map that takes each function from to to the characteristic function of its graph.

* An equivalent definition of the analytical hierarchy on Baire space is given by defining the analytical hierarchy of formulas using a functional version of second-order arithmetic ; then the analytical hierarchy on subsets of Cantor space can be defined from the hierarchy on Baire space.

* John Cantor ( 26-27 years old )-by foot and raft from Alaska / Yukon border to Kotzebue Sound ( 2012 ) in 31 days, 13 hours, 23 minutes.

'' My impassioned plea for civil rights created a landslide of correspondence and one sponsor even asked me to consider replacing the Eddie Cantor comedy hour on a permanent basis.

A fundamental theorem due to Georg Cantor shows that it is possible for infinite sets to have different cardinalities, and in particular the set of real numbers and the set of natural numbers do not have the same cardinal number.

The probability measure on Cantor space, sometimes called the fair-coin measure, is defined so that for any binary string x the set of sequences that begin with x has measure 2 < sup >-| x |</ sup >.

This implies that for each natural number n, the set of sequences f in Cantor space such that f ( n )

On September 19, Cantor Fitzgerald made a pledge to distribute 25 percent of the firm's profits for the next five years, and committed to paying for ten years of health care, for the benefit of the families of its 658 former Cantor Fitzgerald, eSpeed, and TradeSpark employees ( profits which would otherwise have been distributed to the Cantor Fitzgerald partners ).

On September 2, 2004, Cantor filed a civil lawsuit against the Kingdom of Saudi Arabia for allegedly providing money to the hijackers and Al Qaeda, one of a number of organizations to do so.

In 1904, the Royal Society awarded Cantor its Sylvester Medal, the highest honor it can confer for work in mathematics.

Kronecker, who headed mathematics at Berlin until his death in 1891, became increasingly uncomfortable with the prospect of having Cantor as a colleague, perceiving him as a " corrupter of youth " for teaching his ideas to a younger generation of mathematicians.

Cantor came to believe that Kronecker's stance would make it impossible for Cantor ever to leave Halle.

Soon after that second hospitalization, Cantor's youngest son Rudolph died suddenly ( while Cantor was delivering a lecture on his views on Baconian theory and William Shakespeare ), and this tragedy drained Cantor of much of his passion for mathematics.

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 ).

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.

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.

Eddie and Ida Cantor were seen in a brief prologue and epilogue set in a projection room, where they are watching Brasselle in action ; at the end of the film Eddie tells Ida, " I never looked better in my life "... and gives the audience a knowing, incredulous look.

He was in a position of authority at Lincoln Cathedral in 1508, according to records there, and was employed at Durham Cathedral as Cantor or Master of the singing boys, and to provide music for the Lady Chapel, in 1513 ; no further records survive of his life.

`` It is as though '', I said on the historic three-hour, coast-to-coast radio broadcast which I bought ( following Father Coughlin and pre-empting the Eddie Cantor, Manhattan Merry-go-round and Major Bowes shows ) `` That Man in the White House, like some despot of yore, insisted on reading my diary, raiding my larder and ransacking my lingerie!!

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.

Headquartered in Midtown Manhattan, New York City, Cantor Fitzgerald was formerly based in the World Trade Center and was the company hardest hit by the September 11, 2001 attacks, which killed all 658 of its employees who were in the office at the time ( out of 960 who were based there ).

Frege's attack seems to be directed at certain foundational doctrines then current in Weierstrass's Berlin School, of which Husserl and Cantor cannot be said to be orthodox representatives.

Not long after that, in 1883, Georg Cantor, who attended lectures by Weierstrass, published examples of subsets of the real line known as Cantor sets, which had unusual properties and are now recognized as fractals.

Georg Ferdinand Ludwig Philipp Cantor ( ; ; – January 6, 1918 ) was a German mathematician, best known as the inventor of set theory, which has become a fundamental theory in mathematics.

Some Christian theologians ( particularly neo-Scholastics ) saw Cantor's work as a challenge to the uniqueness of the absolute infinity in the nature of God — on one occasion equating the theory of transfinite numbers with pantheism — a proposition which Cantor vigorously rejected.

Cantor introduced fundamental constructions in set theory, such as the power set of a set A, which is the set of all possible subsets of A.

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

It was here on May 10, 1869, that Stanford drove The Last Spike ( or golden spike ) which is now on display at the Cantor Arts Center at Stanford University, that joined the rails of the transcontinental railroad.

Cantor distinguished three realms of infinity: ( 1 ) the infinity of God ( which he called the " absolutum "), ( 2 ) the infinity of reality ( which he called " nature ") and ( 3 ) the transfinite numbers and sets of mathematics.

Under this aspect, the inclusion of actual infinity into mathematics, which explicitly started with G. Cantor only towards the end of the last century, seems displeasing.

It was suggested to him as an alternate form of Russell's paradox, which he had devised to show that set theory as it was used by Georg Cantor and Gottlob Frege contained contradictions.

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.

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.

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 ).