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...

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...

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...

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...

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...

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...

shown that the set of algebraic numbers is countable (for example, see Cantor's first set theory article § The proofs). Since the set of algebraic numbers...

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...

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...

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

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...

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...

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...

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

cardinality of the set of integers is strictly smaller than that of the set of real numbers (see Cantor's first uncountability proof and Cantor's diagonal argument)...

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

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...

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...

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...

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

than the set itself (or informally, the power set must be larger than the original set). In particular, Cantor's theorem shows that the power set of a countably...

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...

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...

logic itself." The second group of logicians, the set-theorists, emerged with Georg Cantor's "set theory" (1870–1890) but were driven forward partly as a...

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...

In set theory, the axiom of limitation of size was proposed by John von Neumann in his 1925 axiom system for sets and classes. It formalizes the limitation...

In his work on set theory, Georg Cantor denoted the collection of all cardinal numbers by the last letter of the Hebrew alphabet, ת (transliterated as...