Английская Википедия:Classification theorem

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Шаблон:Short description Шаблон:Unreferenced In mathematics, a classification theorem answers the classification problem "What are the objects of a given type, up to some equivalence?". It gives a non-redundant enumeration: each object is equivalent to exactly one class.

A few issues related to classification are the following.

  • The equivalence problem is "given two objects, determine if they are equivalent".
  • A complete set of invariants, together with which invariants are Шаблон:Clarify span solves the classification problem, and is often a step in solving it.
  • A Шаблон:Clarify span (together with which invariants are realizable) solves both the classification problem and the equivalence problem.
  • A canonical form solves the classification problem, and is more data: it not only classifies every class, but provides a distinguished (canonical) element of each class.

There exist many classification theorems in mathematics, as described below.

Geometry

Algebra

Linear algebra

Analysis

Complex analysis

Mathematical physics

See also

Партнерские ресурсы
Криптовалюты
Магазины
Хостинг
Разное

Источник — http://wikihandbk.com/ruwiki/index.php?title=Английская_Википедия:Classification_theorem&oldid=13979598