Guava JavaDocs 中的集合基于不同的 "equivalence relations" 是什么意思？
What do the Guava JavaDocs mean by sets being based on different "equivalence relations"?
番石榴 JavaDocs Sets.SetView.union()（以及 intersection()、difference() 和 symmetricDifference()）提及 "equivalence relations":
Results are undefined if set1 and set2 are sets based on different equivalence relations (as HashSet, TreeSet, and the Map.keySet() of an IdentityHashMap all are).
我很难理解那句话的意思。
词汇表defines "equivalence relation" as reflexive ("a.relation(a) is always true"), symmetric (a1.relation(a2) == a2.relation(a1)) and transitive (a1.relation(a2) && a2.relation(a3) implies a1.relation(a3)) - and refers to Object.equals()' docs. (Unfortunately, the Guava wiki没有详细说明...
但是 Set 的不同类型在这方面有何不同（即等价关系）？好像都继承了equals() from AbstractSet？它与集合包含的对象类型无关（例如 Set<Cow> 与 Set<Chicken>），对吗？
听起来他们指的是 Set 出于某种原因不使用 equals 和 hashCode 来比较元素。最常见的示例是带有自定义 Comparator 的 TreeSet。例如，我们可以有这样的东西：
Set<String> a = new TreeSet<>();
Set<String> b = new TreeSet<>(String.CASE_INSENSITIVE_ORDER);
a和b的并集、交集等未定义，因为a和b定义的元素之间的等价关系不同
Java SE在讲到与equals不一致的顺序时也提到了这种情况（见TreeSet）：
Note that the ordering maintained by a set (whether or not an explicit comparator is provided) must be consistent with equals if it is to correctly implement the Set interface. (See Comparable or Comparator for a precise definition of consistent with equals.) This is so because the Set interface is defined in terms of the equals operation, but a TreeSet instance performs all element comparisons using its compareTo (or compare) method, so two elements that are deemed equal by this method are, from the standpoint of the set, equal. The behavior of a set is well-defined even if its ordering is inconsistent with equals; it just fails to obey the general contract of the Set interface.
番石榴 JavaDocs Sets.SetView.union()（以及 intersection()、difference() 和 symmetricDifference()）提及 "equivalence relations":
Results are undefined if
set1andset2are sets based on different equivalence relations (asHashSet,TreeSet, and theMap.keySet()of anIdentityHashMapall are).
我很难理解那句话的意思。
词汇表defines "equivalence relation" as reflexive ("a.relation(a) is always true"), symmetric (a1.relation(a2) == a2.relation(a1)) and transitive (a1.relation(a2) && a2.relation(a3) implies a1.relation(a3)) - and refers to Object.equals()' docs. (Unfortunately, the Guava wiki没有详细说明...
但是 Set 的不同类型在这方面有何不同（即等价关系）？好像都继承了equals() from AbstractSet？它与集合包含的对象类型无关（例如 Set<Cow> 与 Set<Chicken>），对吗？
听起来他们指的是 Set 出于某种原因不使用 equals 和 hashCode 来比较元素。最常见的示例是带有自定义 Comparator 的 TreeSet。例如，我们可以有这样的东西：
Set<String> a = new TreeSet<>();
Set<String> b = new TreeSet<>(String.CASE_INSENSITIVE_ORDER);
a和b的并集、交集等未定义，因为a和b定义的元素之间的等价关系不同
Java SE在讲到与equals不一致的顺序时也提到了这种情况（见TreeSet）：
Note that the ordering maintained by a set (whether or not an explicit comparator is provided) must be consistent with equals if it is to correctly implement the
Setinterface. (SeeComparableorComparatorfor a precise definition of consistent with equals.) This is so because theSetinterface is defined in terms of theequalsoperation, but aTreeSetinstance performs all element comparisons using itscompareTo(orcompare) method, so two elements that are deemed equal by this method are, from the standpoint of the set, equal. The behavior of a set is well-defined even if its ordering is inconsistent with equals; it just fails to obey the general contract of theSetinterface.