**Cantor's theorem** — Note: in order to fully understand this article you may want to refer to the set theory portion of the table of mathematical symbols. In elementary set theory, Cantor s theorem states that, for any set A , the set of all subsets of A (the power… … Wikipedia

**Cantor's paradox** — In set theory, Cantor s paradox is the theorem that there is no greatest cardinal number, so that the collection of infinite sizes is itself infinite. Furthermore, it follows from this fact that this collection is not a set but a proper class; in … Wikipedia

**Cantor's diagonal argument** — An illustration of Cantor s diagonal argument for the existence of uncountable sets. The sequence at the bottom cannot occur anywhere in the list of sequences above. Cantor s diagonal argument, also called the diagonalisation argument, the… … Wikipedia

**Cantor's paradox** — The contradiction arising if we compare for size the set of all sets, and its own power set . By Cantor s theorem the power set must be bigger (contain more members). But it is itself a subset of the set of all sets, and so cannot be bigger. The… … Philosophy dictionary

**Cantor's first uncountability proof** — Georg Cantor s first uncountability proof demonstrates that the set of all real numbers is uncountable. Cantor formulated the proof in December 1873 and published it in 1874 in Crelle s Journal [cite… … Wikipedia

**Controversy over Cantor's theory** — In mathematical logic, the theory of infinite sets was first developed by Georg Cantor. Although this work has found wide acceptance in the mathematics community, it has been criticized in several areas by mathematicians and philosophers. Cantor… … Wikipedia

**König's theorem (set theory)** — For other uses, see König s theorem. In set theory, König s theorem (named after the Hungarian mathematician Gyula König) colloquially states that if the axiom of choice holds, I is a set, mi and ni are cardinal numbers for every i in I , and m i … Wikipedia

**Theorem** — The Pythagorean theorem has at least 370 known proofs[1] In mathematics, a theorem is a statement that has been proven on the basis of previously established statements, such as other theorems, and previously accepted statements … Wikipedia

**Cantor , Georg Ferdinand Ludwig Philipp** — (1845–1918) German mathematician The son of a prosperous merchant of St. Petersburg, at that time the capital of Russia, Cantor was educated at the University of Berlin where he completed his PhD in 1868. In 1870 he joined the faculty of the… … Scientists

**Cantor set** — In mathematics, the Cantor set, introduced by German mathematician Georg Cantor in 1883 [Georg Cantor (1883) Über unendliche, lineare Punktmannigfaltigkeiten V [On infinite, linear point manifolds (sets)] , Mathematische Annalen , vol. 21, pages… … Wikipedia