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...

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 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...

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...

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...

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...

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...

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...

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

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

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...

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)...

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...

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...

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...

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...

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

concept was first introduced by Georg Cantor in 1872 and he developed set theory in large part to study derived sets on the real line. The derived set of a subset...

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...

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...

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...

ordered sets by building upon the concepts of set theory, arithmetic, and binary relations. Orders are special binary relations. Suppose that P is a set and...

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

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...

equinumerous (see Cantor's first uncountability proof). In his controversial 1878 paper, Cantor explicitly defined the notion of "power" of sets and used it...