User:Grady/Harmonic similarity: Difference between revisions
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== Definition == | == Definition == | ||
=== Pseudo-transitivity === | |||
It should be intuitive that any [[wikipedia:Equivalence_relation|equivalence relation]] follows the [[wikipedia:Transitive_relation|transitive property]]. For example, if x = y and y = z, then x = z. Or in geometry, if A is [[wikipedia:Congruence_(geometry)|congruent]] to B and B is congruent to C, then A is congruent to C. For a more practical example, if Alice's car is the same model as Bob's car, and Bob's car is the same model as Charlie's car, then Alice and Charlie also have the same model of car. | It should be intuitive that any [[wikipedia:Equivalence_relation|equivalence relation]] follows the [[wikipedia:Transitive_relation|transitive property]]. For example, if x = y and y = z, then x = z. Or in geometry, if A is [[wikipedia:Congruence_(geometry)|congruent]] to B and B is congruent to C, then A is congruent to C. For a more practical example, if Alice's car is the same model as Bob's car, and Bob's car is the same model as Charlie's car, then Alice and Charlie also have the same model of car. | ||