Classification theorem: Difference between revisions

Revision as of 11:14, 10 May 2020

Revision as of 19:12, 5 October 2020

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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 related 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 {{clarify span|realizable,|reason=This notion should be introduced.}} solves the classification problem, and is often a step in solving it.

*A computable [[complete set of invariants]] (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.