Mathematical classification systems | Mathematical theorems

Classification theorem

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 realizable, 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. There exist many classification theorems in mathematics, as described below. (Wikipedia).

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From playlist Essence of Group Theory

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