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In mathematics, a complete set of invariants for a classification problem is a collection of maps
, such that x ∼ x ′ {\displaystyle x\sim x'} if and only if f i = f i {\displaystyle f_{i}=f_{i}} for all i {\displaystyle 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
is injective.
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