question marks, boxes, or other symbols. In mathematical set theory, Cantor's theorem is a fundamental result which states that, for any set A {\displaystyle...

numbers 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...

R. A generalized form of the diagonal argument was used by Cantor to prove Cantor's theorem: for every set S, the power set of S—that is, the set of all...

The theorem is named after Felix Bernstein and Ernst Schröder. It is also known as the Cantor–Bernstein theorem or Cantor–Schröder–Bernstein theorem, after...

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...

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...

mathematics and logic, such as Cantor's diagonal argument, Cantor's theorem, Russell's paradox, Gödel's first incompleteness theorem, Turing's solution to the...

|A| ≤ |B| and |B| ≤ |A|, then |A| = |B|. This theorem does not rely on the axiom of choice. Cantor's theorem implies that no set is equinumerous to its power...

Look up Cantor's theorem in Wiktionary, the free dictionary. Cantor's theorem is a fundamental result in mathematical set theory. Cantor's theorem may also...

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

Cantor's intersection theorem refers to two closely related theorems in general topology and real analysis, named after Georg Cantor, about intersections...

In order theory and model theory, branches of mathematics, Cantor's isomorphism theorem states that every two countable dense unbounded linear orders are...

Heine–Cantor theorem states that a continuous function between two metric spaces is uniformly continuous if its domain is compact. The theorem is named...

class. Zermelo's paper may be 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...

sets. Cantor gave two proofs that the cardinality of the set of integers is strictly smaller than that of the set of real numbers (see Cantor's first...

Burnside's lemma Cantor's theorem Cantor–Bernstein–Schroeder theorem Cayley's formula Cayley's theorem Clique problem (to do) Compactness theorem (very compact...

the power set must be larger than the original set). In particular, Cantor's theorem shows that the power set of a countably infinite set is uncountably...

cardinality of this set (P2820) (see uses) Aleph number Beth number Cantor's paradox Cantor's theorem Countable set Counting Ordinality Pigeonhole principle "Cardinality...

\kappa } . Thus, Kőnig's theorem gives us an alternate proof of Cantor's theorem. (Historically of course Cantor's theorem was proved much earlier.)...

following theorems: Cantor's diagonal argument (the earliest) Cantor's theorem Russell's paradox Diagonal lemma Gödel's first incompleteness theorem Tarski's...

of all sets, provided that both exist. However, this conflicts with Cantor's theorem that the power set of any set (whether infinite or not) always has...

must satisfy the sentence saying the real numbers are uncountable. Cantor's theorem states that some sets are uncountable. This counterintuitive situation...

Cantor proved that the real numbers were uncountable; in 1891, he proved by his diagonal argument the more general result known as Cantor's theorem:...

{P}}(A)} . A proof 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...

algorithm to solve any first-order problem in Euclidean geometry. Cantor's theorem Artin, Emil (1988) [1957], Geometric Algebra, Wiley Classics Library...

This theorem is proved using Cantor's first uncountability proof, which differs from the more familiar proof using his diagonal argument. Cantor introduced...

universal set, so it must be that Cantor's theorem (in its original form) does not hold in NF. Indeed, the proof of Cantor's theorem uses the diagonalization argument...

theory, for instance Cantor's paradox and the Burali-Forti paradox, and did not believe that they discredited his theory. Cantor's paradox can actually...

set P(S). Georg Cantor proved that the power set is always larger than the set, i.e., |P(S)| > |S|. A special case of Cantor's theorem is that the set...

also known as a "helping theorem" or an "auxiliary theorem". In many cases, a lemma derives its importance from the theorem it aims to prove; however...