In mathematics, a complete set of invariants for a classification problem is a collection of maps <math>f_i : X \to Y_i \,</math> (where X is the collection of objects being classified, up to some equivalence relation, and the <math>Y_i</math> are some sets), such that <math>x</math> ∼ <math>x'</math> if and only if <math>f_i(x) = f_i(x')</math> for all i.

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dbpprop:abstract
  • In mathematics, a complete set of invariants for a classification problem is a collection of maps <math>f_i : X \to Y_i \,</math> (where X is the collection of objects being classified, up to some equivalence relation, and the <math>Y_i</math> are some sets), such that <math>x</math> ∼ <math>x'</math> if and only if <math>f_i(x) = f_i(x')</math> for all i. In words, such that two objects are equivalent if and only if all invariants are equal. Symbolically, a complete set of invariants is a collection of maps such that <math>\prod f_i : (X/\sim) \to \prod Y_i</math> is injective.
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rdfs:comment
  • In mathematics, a complete set of invariants for a classification problem is a collection of maps <math>f_i : X \to Y_i \,</math> (where X is the collection of objects being classified, up to some equivalence relation, and the <math>Y_i</math> are some sets), such that <math>x</math> ∼ <math>x'</math> if and only if <math>f_i(x) = f_i(x')</math> for all i.
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  • Complete set of invariants
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