Cantor's first set theory article contains Georg Cantor's first theorems of transfinite set theory, which studies infinite sets and their properties....

and their arithmetic. Cantor's work is of great philosophical interest, a fact he was well aware of. Originally, Cantor's theory of transfinite numbers...

philosophers. Cantor's theorem implies that there are sets having cardinality greater than the infinite cardinality of the set of natural numbers. Cantor's argument...

In mathematical set theory, Cantor's theorem is a fundamental result which states that, for any set A {\displaystyle A} , the set of all subsets of A...

theory. After the discovery of paradoxes within naive set theory (such as Russell's paradox, Cantor's paradox and the Burali-Forti paradox), various axiomatic...

In set theory, Cantor's paradox states that there is no set of all cardinalities. This is derived from the theorem that there is no greatest cardinal number...

principles which can be used to form sets. Some believe that Georg Cantor's set theory was not actually implicated in the set-theoretic paradoxes (see Frápolli...

the first to mention the name "Cantor's theorem". Cantor's theorem: "If M is an arbitrary set, then always M < P(M) [the power set of M]. Every set is...

axiomatic set theory. Set theory as conceived by Georg Cantor assumes the existence of infinite sets. As this assumption cannot be proved from first principles...

In set theory, the union (denoted by ∪) of a collection of sets is the set of all elements in the collection. It is one of the fundamental operations...

theorem Cantor's first set theory article Cantor's leaky tent Cantor's paradox Cantor's theorem Cantor–Bendixson rank Cantor–Bendixson theorem Cantor–Bernstein...

immune to the classic paradoxes of naive set theory: Russell's paradox, the Burali-Forti paradox, and Cantor's paradox. Abian & LaMacchia (1978) studied...

mathematics, the power set (or powerset) of a set S is the set of all subsets of S, including the empty set and S itself. In axiomatic set theory (as developed...

knowledge, including Cantor's theory of infinite sets. One potential application of infinite set theory is in genetics and biology. The set of all integers...

In set theory, the intersection of two sets A {\displaystyle A} and B , {\displaystyle B,} denoted by A ∩ B , {\displaystyle A\cap B,} is the set containing...

In the mathematical field of set theory, the continuum means the real numbers, or the corresponding (infinite) cardinal number, denoted by c {\displaystyle...

Axiomatic constructive set theory is an approach to mathematical constructivism following the program of axiomatic set theory. The same first-order language with...

is given in the article Cantor's theorem. As an immediate consequence of this and the Basic Theorem above we have: Proposition — The set P ( N ) {\displaystyle...

In set theory, the Schröder–Bernstein theorem states that, if there exist injective functions f : A → B and g : B → A between the sets A and B, then there...

S is an axiomatic set theory set out by George Boolos in his 1989 article, "Iteration Again". S, a first-order theory, is two-sorted because its ontology...

In set theory, an ordinal number, or ordinal, is a generalization of ordinal numerals (first, second, nth, etc.) aimed to extend enumeration to infinite...

absolute infinite in Cantor's conception of set". Erkenntnis. 42 (3): 375–402. doi:10.1007/BF01129011. JSTOR 20012628. S2CID 122487235. Cantor (1) took the absolute...

time he published "the first axiomatic set theory") laid claim to prior discovery of the antinomy in Cantor's naive set theory. He states: "And yet, even...

on the problems of Zermelo set theory and provided solutions for some of them: A theory of ordinals Problem: Cantor's theory of ordinal numbers cannot...

the real and the algebraic numbers was not possible before Cantor's first set theory article in 1874. Liouville, J. (1844). "Sur les classes très étendues...

the set of algebraic numbers is countable. (See Georg Cantor's first set theory article.) Felix Hausdorff First published in 1914, this was the first comprehensive...

the set of all prefilters on a set) so in such cases this article uses whatever notation is most self describing or easily remembered. The theory of filters...

), and every point not in the Cantor set is in one of these intervals, so its derivative is 0 outside of the Cantor set. On the other hand, it has no...

Scott–Potter set theory Constructive set theory Zermelo set theory General set theory Non-well-founded set theory List of first-order theories § Set theories Holmes...

The set of rational numbers is countable, so almost all real numbers are irrational. Georg Cantor's first set theory article proved that the set of algebraic...