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.

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 ).

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.

* 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.

In addition to film and radio, Cantor recorded for Hit of the Week Records, then again for Columbia, for Banner and Decca and various small labels.

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.

If A and B are recursively enumerable sets then A ∩ B, A ∪ B and A × B ( with the ordered pair of natural numbers mapped to a single natural number with the Cantor pairing function ) are recursively enumerable sets.

If A and B are recursive sets then A ∩ B, A ∪ B and the image of A × B under the Cantor pairing function are recursive sets.

# ( Cantor – Bendixson theorem ) If X is Polish then any closed subset of X can be written as the disjoint union of a perfect subset and a countable subset.

The House Majority Leader position instead went to then Majority Whip Roy Blunt, though both Dreier and then Deputy Majority Whip Eric Cantor of Virginia shared in some duties.

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.

If the axiom holds then there is also a well ordering of Cantor space.

Continuing indefinitely with this removal, the Smith – Volterra – Cantor set is then the set of points that are never removed.

We then translate this function to the interval 5 / 8 so that the resulting function, which we call f < sub > 1 </ sub >, is nonzero only on the middle interval of the complement of the Smith – Volterra – Cantor set.

Volterra's function then results by repeating this procedure for every interval removed in the construction of the Smith – Volterra – Cantor set ; in other words, the function V is the limit of the sequence of functions f < sub > 1 </ sub >, f < sub > 2 </ sub >, ...

If one were to repeat the construction of Volterra's function with the ordinary measure-0 Cantor set C in place of the " fat " ( positive-measure ) Cantor set S, one would obtain a function with many similar properties, but the derivative would then be discontinuous on the measure-0 set C instead of the positive-measure set S, and so the resulting function would have an integrable derivative.

In mathematics, the Heine – Cantor theorem, named after Eduard Heine and Georg Cantor, states that if M and N are metric spaces and M is compact then every continuous function

The effect of the question mark function on can then be understood as mapping the second interpretation of a string to the first interpretation of the same string, just as the Cantor function can be understood as mapping a triadic base 3 representation to a base 2 representation.

Three years later, he moved to New York City and was hired as a singer and straight man on The Eddie Cantor Show, then becoming a CBS Radio staff announcer.

If is a set of subsets of the natural numbers, then the set ( using the Cantor pairing function ) is required to be recursively enumerable.

The implications of the infinite void were revolutionary ; to have pursued them would have threatened the singular relationship of man and this natural world to God ( Cantor 2001 ); in it he treated theology mathematically.

In Waguespack and Cantor ( 1996 ), the authors point out that JIT would require a significant change in the supplier / refiner relationship, but the changes in inventories in the oil industry exhibit none of those tendencies.

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.

'' 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.

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.

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.

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

At that Congress, Cantor renewed his friendship and correspondence with Dedekind.

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.

The principle that cardinal number was to be characterized in terms of one-to-one correspondence had previously been used to great effect by Georg Cantor, whose writings Frege knew.

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.

Cantor equated the Absolute Infinite with God.

Some believe that Georg Cantor's set theory was not actually implicated by these paradoxes ( see Frápolli 1991 ); one difficulty in determining this with certainty is that Cantor did not provide an axiomatization of his system.

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 >.

Each of these strings p < sub > i </ sub > determines a subset S < sub > i </ sub > of Cantor space ; the set S < sub > i </ sub > contains all sequences in cantor space that begin with p < sub > i </ sub >.

World Trade Center | One World Trade Center, the building with the antenna to the left, included the corporate headquarters of Cantor Fitzgerald.

Seconds after Cantor's building was struck by the plane, a Goldman Sachs server issued an alert saying that its trading system had gone offline because it wasn't able to connect with a Cantor server.

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.

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

During his honeymoon in the Harz mountains, Cantor spent much time in mathematical discussions with Richard Dedekind, whom he had met two years earlier while on Swiss holiday.

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.

( Konig is now remembered as having only pointed out that some sets cannot be well-ordered, in disagreement with Cantor.

From 1905, Cantor corresponded with his British admirer and translator Philip Jourdain on the history of set theory and on Cantor's religious ideas.

Cantor starts his second construction with any sequence of real numbers.

During this time, Staind acquired a concert slot with Limp Bizkit through longtime friend Justin Cantor.

Georg Cantor is the most significant mathematician who defended actual infinities, equating the Absolute Infinite with God.

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.

In the sound era McCarey ventured into feature-film direction, working with many of the biggest stars of the era, including Gloria Swanson ( Indiscreet, 1931 ), Eddie Cantor ( The Kid From Spain, 1932 ), the Marx Brothers ( Duck Soup, 1933 ), W. C. Fields ( Six of a Kind, 1934 ), Mae West ( Belle of the Nineties, 1934 ), and Harold Lloyd ( The Milky Way, 1936 ).

Starting with version 4. 4, the KDE Software Compilation contains Cantor -- which can interface with Maxima ( along with Sage, R, and Kalgebra ).