equivalence relation
Sameness under consideration
An equivalence relation is a mathematical relationship between elements of a set that satisfies three properties: reflexivity (each element relates to itself), symmetry (if A relates to B, then B relates to A), and transitivity (if A relates to B and B relates to C, then A relates to C).
Equality is the prototypical example, but "same age as" or "congruent to" also qualify.
Equivalence relations partition sets into equivalence classes—groups of elements all related to each other.
Quality of self-reference
- symmetryInvariance under transformation
- transitivityRelation that chains through
- partitionBarrier separating spaces
- set theoryMathematics of abstract collections
congruence · axiom · predicate · well-defined · canonical · kernel
State of agreement
- isomorphismStructure-preserving bijective map
- kernelSeed or essential core
- quotient ringRing of cosets
- idealStandard of perfection
Same status for all
- similarityState of being alike
- parallelismMatching structural elements
- isometryDistance-preserving map
Barrier separating spaces
- blocksObstructs or sections
- cellsBasic biological units
- representativeOne who acts for another
- decompositionBreakdown into simpler parts
orbit · fiber · index · cardinality · counting · classification
reflexivity
Quality of self-reference
- symmetryInvariance under transformation
- transitivityRelation that chains through
- partitionBarrier separating spaces
set theory · congruence · axiom · predicate · well-defined · canonical · kernel
congruence
State of agreement
- isomorphismStructure-preserving bijective map
- kernelSeed or essential core
- quotient ringRing of cosets
equality
Same status for all
- similarityState of being alike
- parallelismMatching structural elements
- isometryDistance-preserving map
partition
Barrier separating spaces
- blocksObstructs or sections
- cellsBasic biological units
- representativeOne who acts for another
decomposition · orbit · fiber · index · cardinality · counting · classification
- relationsrelationship, connection, link, linkage, reflexive
- equivalencesisomorphism, equal, equals sign, biconditional, if and only if
- groupoids
relation, relative, equivalent, relations, equivocal, equivalence point, equivalence, equivocate, unequivocal