Set theory > Related Articles
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- Absorption [r]: An identity linking a pair of binary operations. [e]
- Aleph-0 [r]: Cardinality (size) of the set of all natural numbers. [e]
- Algebra [r]: A branch of mathematics concerning the study of structure, relation and quantity. [e]
- Axiom of choice [r]: Set theory asserting that if S is a set of disjoint, non-empty sets, then there exists a set containing exactly one member from each member of S. [e]
- Bertrand Russell [r]: (1872–1970) British analytic philosopher, logician, essayist and political activist. [e]
- Cantor's diagonal argument [r]: Proof due to Georg Cantor showing that there are uncountably many sets of natural numbers. [e]
- Cardinal number [r]: The generalization of natural numbers (as means to count the elements of a set) to infinite sets. [e]
- Cartesian product [r]: The set of ordered pairs whose elements come from two given sets. [e]
- Characteristic function [r]: A function on a set which takes the value 1 on a given subset and 0 on its complement. [e]
- Complement (set theory) [r]: The set containing those elements of a set (or "universal" set) which are not contained in a given set. [e]
- Computer science [r]: The study of how computers work, and the algorithms, data structures and design principles used in their operation and programming. [e]
- Continuum hypothesis [r]: A statement about the size of the continuum, i.e., the number of elements in the set of real numbers. [e]
- Countable set [r]: A set with as many elements as there are natural numbers, or less. [e]
- Discrete mathematics [r]: The disciplines within mathematics that study discrete objects: combinatorics, graph theory, number theory, mathematical logic, … [e]
- Disjoint union [r]: A set containing a copy of each of a family of two or more sets, so that the copies do not overlap. [e]
- Distributivity [r]: A relation between two binary operations on a set generalising that of multiplication to addition: a(b+c)=ab+ac. [e]
- Element (disambiguation) [r]: Add brief definition or description
- Filter (mathematics) [r]: A family of subsets of a given set which has properties generalising the notion of "almost all natural numbers". [e]
- Finite set [r]: The number of its elements is a natural number (0,1,2,3,...) [e]
- Function (mathematics) [r]: A relationship dependence between two quantities, one of which is given (the independent variable, argument, or input) and the other (the dependent variable, value, or output) is uniquely defined by the input. [e]
- Hash table [r]: Add brief definition or description
- Inclusion-exclusion principle [r]: Principle that, if A and B are finite sets, the number of elements in the union of A and B can be obtained by adding the number of elements in A to the number of elements in B, and then subtracting from this sum the number of elements in the intersection of A and B. [e]
- Intersection [r]: The set of elements that are contained in all of a given family of two or more sets. [e]
- Kernel of a function [r]: The equivalence relation on the domain of a function defined by elements having the same function value: the partition of the domain into fibres of a function. [e]
- Kurt Gödel [r]: (1906-1978) Austrian born American mathematician, most famous for proving that in any logical system rich enough to describe naturals, there are always statements that are true but impossible to prove within the system. [e]
- Logical positivism [r]: A school of philosophy that combines positivism—which states that the only authentic knowledge is scientific knowledge—with some king of logical analysis, which is similar, but not the same as logicism. [e]
- Logic [r]: The study of the standards and practices of correct argumentation. [e]
- Mathematics [r]: The study of quantities, structures, their relations, and changes thereof. [e]
- Music [r]: The art of structuring time by combining sound and silence into rhythm and harmonies. [e]
- Number [r]: One of the fundamental concepts of mathematics, used for such purposes as counting, ordering, and measuring. [e]
- Partition (mathematics) [r]: Concepts in mathematics which refer either to a partition of a set or an ordered partition of a set, or a partition of an integer, or a partition of an interval. [e]
- Pointed set [r]: A set together with a distinguished element, known as the base point. [e]
- Power set [r]: The set of all subsets of a given set. [e]
- Relation composition [r]: Formation of a new relation S o R from two given relations R and S, having as its most well-known special case the composition of functions. [e]
- Set (mathematics) [r]: Informally, any collection of distinct elements. [e]
- Sigma algebra [r]: A formal mathematical structure intended among other things to provide a rigid basis for measure theory and axiomatic probability theory. [e]
- Singleton set [r]: A set with exactly one element. [e]
- Subset [r]: A set containing only elements of a given set. [e]
- Symmetric difference [r]: The set of elements that lie in exactly one of two sets. [e]
- Topology [r]: A branch of mathematics that studies the properties of objects that are preserved through continuous deformations (such as stretching, bending and compression). [e]
- Transfinite number [r]: An infinite number, either a cardinal number or an ordinal number. [e]
- Transitive relation [r]: A relation with the property that if x→y and y→z then x→z. [e]
- Union [r]: The set of elements which are in at least one of a given family of sets. [e]
