**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-Bendixson theorem** — noun A theorem which states that a closed set in a Polish space is the disjoint union of a countable set and a perfect set. From the Cantor Bendixson theorem it can be deduced that an uncountable set in must have an uncountable number of limit… … Wiktionary

**Cantor–Bernstein–Schroeder theorem** — In set theory, the Cantor–Bernstein–Schroeder theorem, named after Georg Cantor, Felix Bernstein, and Ernst Schröder, states that, if there exist injective functions f : A → B and g : B → A between the sets A and B , then there exists a bijective … 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

**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'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** — ist der Name von Bernard Gerald Cantor (1916–1996), US amerikanischer Unternehmer und Kunstmäzen, Firmengründer der Cantor Fitzgerald Eddie Cantor (1892–1964), US amerikanischer Entertainer Eric Cantor (* 1963), US amerikanischer Politiker Georg… … Deutsch Wikipedia

**Cantor space** — In mathematics, the term Cantor space is sometimes used to denotethe topological abstraction of the classical Cantor set:A topological space is aCantor space if it is homeomorphic to the Cantor set.The Cantor set itself is of course a Cantor… … Wikipedia