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Projection (mathematics) – Mapping equal to its square under mapping composition; Projection (measure theory) Projection (linear algebra) – Idempotent linear transformation from a vector space to itself; Projection (relational algebra) – Operation that restricts a relation to a specified set of attributes
Every set is a projective object in Set (assuming the axiom of choice). The finitely presentable objects in Set are the finite sets. Since every set is a direct limit of its finite subsets, the category Set is a locally finitely presentable category. If C is an arbitrary category, the contravariant functors from C to Set are often an important ...
A set of polygons in an Euler diagram This set equals the one depicted above since both have the very same elements.. In mathematics, a set is a collection of different [1] things; [2] [3] [4] these things are called elements or members of the set and are typically mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other ...
Cardinal functions are widely used in topology as a tool for describing various topological properties. [4] [5] Below are some examples.(Note: some authors, arguing that "there are no finite cardinal numbers in general topology", [6] prefer to define the cardinal functions listed below so that they never take on finite cardinal numbers as values; this requires modifying some of the definitions ...
In mathematical logic, an alternative set theory is any of the alternative mathematical approaches to the concept of set and any alternative to the de facto standard set theory described in axiomatic set theory by the axioms of Zermelo–Fraenkel set theory.
In mathematics, the limit of a sequence of sets,, … (subsets of a common set ) is a set whose elements are determined by the sequence in either of two equivalent ways: (1) by upper and lower bounds on the sequence that converge monotonically to the same set (analogous to convergence of real-valued sequences) and (2) by convergence of a sequence of indicator functions which are themselves ...
In set theory, a standard model for a theory T is a model M for T where the membership relation ∈ M is the same as the membership relation ∈ of a set theoretical universe V (restricted to the domain of M). In other words, M is a substructure of V.
And we can map the powerset of into the Cantor set, a subset of the real numbers. So statements about H ℵ 1 {\displaystyle H_{\aleph _{1}}} can be converted into statements about the reals. Therefore, H ℵ 1 ⊂ L ( R ) {\displaystyle H_{\aleph _{1}}\subset L(R)} , where L ( R ) is the smallest transitive inner model of ZF containing all the ...