In universal algebra and lattice theory, a tolerance relation on an algebraic structure is a reflexive symmetric relation that is compatible with all operations of the structure. Thus a tolerance is like a congruence, except that the assumption of transitivity is dropped. On a set, an algebraic structure with empty family of operations, tolerance relations are simply reflexive symmetric relations. A set that possesses a tolerance relation can be described as a tolerance space. Tolerance relations provide a convenient general tool for studying indiscernibility/indistinguishability phenomena. The importance of those for mathematics had been first recognized by Poincaré.
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| - علاقة تسامح (رياضيات) (ar)
- Relation de tolérance (fr)
- 허용 관계 (ko)
- Tolerance relation (en)
- 相容关系 (zh)
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| - في الرياضيات، العلاقة التسامحية (بالإنجليزية: Tolerance Relation) هي علاقة انعكاسية وتناظرية، لا يجب أن تكون متعدية. (ar)
- En mathématiques, une relation de tolérance est une relation réflexive, symétrique mais non transitive. L'ensemble décrit par ce type de relation est un espace de tolérance. (fr)
- In universal algebra and lattice theory, a tolerance relation on an algebraic structure is a reflexive symmetric relation that is compatible with all operations of the structure. Thus a tolerance is like a congruence, except that the assumption of transitivity is dropped. On a set, an algebraic structure with empty family of operations, tolerance relations are simply reflexive symmetric relations. A set that possesses a tolerance relation can be described as a tolerance space. Tolerance relations provide a convenient general tool for studying indiscernibility/indistinguishability phenomena. The importance of those for mathematics had been first recognized by Poincaré. (en)
- 在泛代数和格理论中，相容关系（tolerance relation）是指被代数结构的每个运算所保持的自反对称关系。是同余关系去掉传递性的要求而得到的概念。 具体内容参考：左孝凌离散数学，石纯一数理逻辑与集合论，对“相容关系与覆盖”的再认识。注意，左孝凌和再认识一文对完全覆盖的定义是不同的，左文定义的完全覆盖和相容关系是一一对应的，而再认识一文定义的完全覆盖和相容关系不是一一对应的。 (zh)
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| - في الرياضيات، العلاقة التسامحية (بالإنجليزية: Tolerance Relation) هي علاقة انعكاسية وتناظرية، لا يجب أن تكون متعدية. (ar)
- En mathématiques, une relation de tolérance est une relation réflexive, symétrique mais non transitive. L'ensemble décrit par ce type de relation est un espace de tolérance. (fr)
- In universal algebra and lattice theory, a tolerance relation on an algebraic structure is a reflexive symmetric relation that is compatible with all operations of the structure. Thus a tolerance is like a congruence, except that the assumption of transitivity is dropped. On a set, an algebraic structure with empty family of operations, tolerance relations are simply reflexive symmetric relations. A set that possesses a tolerance relation can be described as a tolerance space. Tolerance relations provide a convenient general tool for studying indiscernibility/indistinguishability phenomena. The importance of those for mathematics had been first recognized by Poincaré. (en)
- 보편 대수학과 격자 이론에서 허용 관계(영어: tolerance relation)는 대수 구조의 연산과 호환되는 반사 대칭 관계이다. 즉, 합동 관계에서 추이성 조건을 없애 얻는 개념이다. 허용 관계에 대한 몫 대수는 합동 관계에 대한 몫 대수를 일반화한다. 합동 관계와 달리, 허용 관계에 대한 몫 대수는 존재하지 않을 수 있으며, 몫 대수는 (만약 존재한다면) 항등식들을 보존할 필요가 없다. (ko)
- 在泛代数和格理论中，相容关系（tolerance relation）是指被代数结构的每个运算所保持的自反对称关系。是同余关系去掉传递性的要求而得到的概念。 具体内容参考：左孝凌离散数学，石纯一数理逻辑与集合论，对“相容关系与覆盖”的再认识。注意，左孝凌和再认识一文对完全覆盖的定义是不同的，左文定义的完全覆盖和相容关系是一一对应的，而再认识一文定义的完全覆盖和相容关系不是一一对应的。 (zh)
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