Search results
Results From The WOW.Com Content Network
Correspondence (algebraic geometry) In algebraic geometry, a correspondence between algebraic varieties V and W is a subset R of V × W, that is closed in the Zariski topology. In set theory, a subset of a Cartesian product of two sets is called a binary relation or correspondence; thus, a correspondence here is a relation that is defined by ...
e. A bijection, bijective function, or one-to-one correspondence between two mathematical sets is a function such that each element of the second set (the codomain) is mapped to from exactly one element of the first set (the domain ). Equivalently, a bijection is a relation between two sets such that each element of either set is paired with ...
Glossary of mathematical symbols. A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation between mathematical objects, or for structuring the other symbols that occur in a formula. As formulas are entirely constituted with symbols of various ...
t. e. In mathematics, a field is a set on which addition, subtraction, multiplication, and division are defined and behave as the corresponding operations on rational and real numbers. A field is thus a fundamental algebraic structure which is widely used in algebra, number theory, and many other areas of mathematics.
Correspondence (algebraic geometry), between two algebraic varieties. Corresponding sides and corresponding angles, between two polygons. Correspondence (category theory), the opposite of a profunctor. Correspondence (von Neumann algebra) or bimodule, a type of Hilbert space. Correspondence analysis, a multivariate statistical technique.
Definition 1: | A | = | B Two sets A and B have the same cardinality if there exists a bijection (a.k.a., one-to-one correspondence) from A to B, that is, a function from A to B that is both injective and surjective. Such sets are said to be equipotent, equipollent, or equinumerous. This relationship can also be denoted A ≈ B or A ~ B.
Countable set. In mathematics, a set is countable if either it is finite or it can be made in one to one correspondence with the set of natural numbers. [a] Equivalently, a set is countable if there exists an injective function from it into the natural numbers; this means that each element in the set may be associated to a unique natural number ...
Dual space. In mathematics, any vector space has a corresponding dual vector space (or just dual space for short) consisting of all linear forms on together with the vector space structure of pointwise addition and scalar multiplication by constants. The dual space as defined above is defined for all vector spaces, and to avoid ambiguity may ...