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The 54 pages that link to Equivalence relation, each with the reason it gives.

• Rational numberRelated: Different integer fractions represent the same rational number when cross-products agree.

• Axiom of choiceRelated: Selecting one representative from every class is a standard choice-dependent construction.

• SymmetryRelated: Symmetry transformations can identify configurations as equivalent without making them identical.

• Homogeneous coordinatesRelated: Projective coordinates identify all nonzero scalar multiples as equivalent representations.

• CardinalityRelated: Bijection partitions sets into classes of equal cardinality.

• Quotient groupRelated: Membership in the same coset defines the equivalence classes used in the quotient.

• Invariant (mathematics)Related: Transformations often define equivalence classes whose members share invariant properties.

• Abstract algebraRelated: Quotient structures arise by treating elements related by a compatible equivalence as indistinguishable.

• DefinitionRelated: These defining properties let mathematicians construct and reason about equivalence classes.

• IsomorphismRelated: Being isomorphic partitions structures into classes considered equivalent under their chosen features.

• Quotient ringRelated: The quotient groups together elements differing by members of the chosen ideal.

• CosetRelated: Membership in the same coset defines an equivalence relation on group elements.

• Orbit-stabilizer theoremRelated: Having the same image of a point partitions group elements into equal-sized classes.

• Lagrange's theoremRelated: Cosets partition a group because membership in the same coset defines an equivalence relation.

• AbstractionRelated: Treating objects as equivalent can abstract away their differences.

• MultisetRelated: Two listings represent the same multiset when their element counts agree, regardless of order.

• Quotient spaceRelated: Vectors are grouped precisely when their difference belongs to the chosen subspace.

• HomotopyRelated: Homotopy partitions maps into classes of continuously deformable maps.

• Cardinal numberRelated: Having the same cardinality partitions sets into size-equivalence classes.

• CokernelRelated: The quotient identifies codomain elements whose difference lies in the image.

• Stirling numbers of the second kindRelated: Every partition corresponds to an equivalence relation whose classes are its blocks.

• Burnside's lemmaRelated: Being in the same orbit is an equivalence relation on the acted-on set.

• CombinationRelated: Treating reordered selections as identical groups ordered lists into equivalence classes.

• Partition of a setRelated: Its equivalence classes form a partition of the underlying set.

• Uniqueness of solutionsRelated: Some mathematical problems treat solutions as equivalent, changing what uniqueness means.

• Bell numberRelated: Each set partition corresponds uniquely to an equivalence relation on the same set.

• Pólya enumeration theoremRelated: Being related by a symmetry determines which configurations count as the same.

• Ring theoryRelated: Congruences use equivalence relations compatible with ring operations.

• Set (abstract data type)Related: Implementations need a consistent rule for deciding when two candidate elements count as the same.

• XNOR gateRelated: For two binary inputs, XNOR outputs 1 exactly when their values are equal.

• Fundamental theorem on homomorphismsRelated: Having equal images partitions the domain into the cosets used in the quotient.

• Standard part functionRelated: Infinitesimal closeness groups finite hyperreals around the same real value.