uncountable set
51Irrational number — In mathematics, an irrational number is any real number that is not a rational number that is, it is a number which cannot be expressed as a fraction m / n , where m and n are integers, with n non zero. Informally, this means numbers that cannot… …
52Second-order logic — In logic and mathematics second order logic is an extension of first order logic, which itself is an extension of propositional logic.[1] Second order logic is in turn extended by higher order logic and type theory. First order logic uses only… …
53Outline of logic — The following outline is provided as an overview of and topical guide to logic: Logic – formal science of using reason, considered a branch of both philosophy and mathematics. Logic investigates and classifies the structure of statements and… …
54Gödel's completeness theorem — is a fundamental theorem in mathematical logic that establishes a correspondence between semantic truth and syntactic provability in first order logic. It was first proved by Kurt Gödel in 1929. A first order formula is called logically valid if… …
55Aleph number — In the branch of mathematics known as set theory, the aleph numbers are a sequence of numbers used to represent the cardinality (or size) of infinite sets. They are named after the symbol used to denote them, the Hebrew letter aleph (aleph).The… …
56Constructive analysis — In mathematics, constructive analysis is mathematical analysis done according to the principles of constructive mathematics. This contrasts with classical analysis, which (in this context) simply means analysis done according to the (ordinary)… …
57Sequential space — In topology and related fields of mathematics, a sequential space is a topological space that satisfies a very weak axiom of countability. Sequential spaces are the most general class of spaces for which sequences suffice to determine the… …
58Cocountable topology — The cocountable topology or countable complement topology on any set X consists of the empty set and all cocountable subsets of X, that is all sets whose complement in X is countable. It follows that the only closed subsets are X and the… …
59First-countable space — In topology, a branch of mathematics, a first countable space is a topological space satisfying the first axiom of countability . Specifically, a space, X , is said to be first countable if each point has a countable neighbourhood basis (local… …
60Cantor-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… …
