Set theory | Abstract algebra | Closure operators

Closure (mathematics)

In mathematics, a subset of a given set is closed under an operation of the larger set if performing that operation on members of the subset always produces a member of that subset. For example, the natural numbers are closed under addition, but not under subtraction: 1 − 2 is not a natural number, although both 1 and 2 are. Similarly, a subset is said to be closed under a collection of operations if it is closed under each of the operations individually. The closure of a subset is the result of a closure operator applied to the subset. The closure of a subset under some operations is the smallest subset that is closed under these operations. It is often called the span (for example linear span) or the generated set. (Wikipedia).

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Closed Intervals, Open Intervals, Half Open, Half Closed

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From playlist Calculus

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Galois theory: Algebraic closure

This lecture is part of an online graduate course on Galois theory. We define the algebraic closure of a field as a sort of splitting field of all polynomials, and check that it is algebraically closed. We hen give a topological proof that the field C of complex numbers is algebraically

From playlist Galois theory

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Javascript Closures Tutorial - What makes Javascript Weird...and Awesome Pt 3

What is a closure? In this Javascript Tutorial, we're going to be learning about closures - our 3rd most misunderstood concept of Javascript. Watch the full playlist: https://www.youtube.com/playlist?list=PLoYCgNOIyGABI011EYc-avPOsk1YsMUe_ Hopefully, we're going to break it down enough t

From playlist Javascript Tutorial For Beginners

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Closure of Sets (Allegra's Question)

clarifying the idea of closure of a set under an operation

From playlist Middle School This Year

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All About Closed Sets and Closures of Sets (and Clopen Sets) | Real Analysis

We introduced closed sets and clopen sets. We'll visit two definitions of closed sets. First, a set is closed if it is the complement of some open set, and second, a set is closed if it contains all of its limit points. We see examples of sets both closed and open (called "clopen sets") an

From playlist Real Analysis

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Commutative Algebra - Integral Closures - part 01 - Basics

This is a video for a second semester graduate algebra class.

From playlist Integral Closures

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Closure and Natural Numbers

Understanding the basic principles of closure for natural numbers

From playlist Geometry

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Reconsidering `functions' in modern mathematics | Arithmetic and Geometry Math Foundations 43

The general notion of `function' does not work in mathematics, just as the general notions of `number' or `sequence' don't work. This video explains the distinction between `closed' and `open' systems, and suggests that mathematical definitions should respect the open aspect of mathemat

From playlist Math Foundations

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Clojure Conj 2012 - Clojure Data Science

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From playlist Clojure Conf 2012

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DDPS | Large Eddy Simulation Reduced Order Models

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From playlist Data-driven Physical Simulations (DDPS) Seminar Series

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J/Link without Java

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From playlist Wolfram Technology Conference 2012

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Stochastic and Deterministic Models for Tropical Convection - Boualem Khouider

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From playlist Mathematical Perspectives on Clouds, Climate, and Tropical Meteorology

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Upscaling and Automation: New Opportunities for Multiscale Systems Modeling

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From playlist SIAM Geosciences Webinar Series

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Metric Spaces - Lectures 11 & 12: Oxford Mathematics 2nd Year Student Lecture

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From playlist Oxford Mathematics Student Lectures - Metric Spaces

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The Essence of Functional Programming

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From playlist Functional Programming

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Gary Gordon and Liz McMahon: Generalizations of Crapo's Beta Invariant

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From playlist Combinatorics

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Super-approximation I - Alireza Salehi Golsefidy

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From playlist Mathematics

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Calculus: Absolute Maximum and Minimum Values

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From playlist Calculus

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Yoshinori Namikawa: Symplectic singularities and nilpotent orbits

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From playlist Algebraic and Complex Geometry

Related pages

Integral domain | Algebraic structure | If and only if | Linear span | Vector space | Algebraic closure | Linear algebra | Convex hull | Operation (mathematics) | Partially ordered set | Ideal (ring theory) | Symmetric relation | Topology | Unary operation | Mathematical analysis | Group (mathematics) | Identity element | Kuratowski closure axioms | Radical of an ideal | Transitive closure | Formal language | Algebraic set | Matroid | Binary relation | Transitive relation | Preorder | Principal ideal | Natural number | Reflexive relation | Set (mathematics) | Function (mathematics) | Field (mathematics) | Symmetric closure | Algebra of sets | Identity (mathematics) | Substructure (mathematics) | Group theory | Cyclic group | Closure operator | Reflexive closure | Subset | Linear combination | Equivalence relation | Subgroup | Ordered pair | Probability theory | Inverse element | Geometry | Ceiling function | Convex set | Transitive set | Commutative ring