STL联系关系容器为什么要定义等价关系? 明明是大小比较

STL关联容器为什么要定义等价关系? 明明是大小比较啊
关联容器自动排序，也就是通过greater或者less来决定顺序。为什么C++语言标准里面说关联容器是通过等价关系来决定顺序呢?

等价关系里面并没有a<b啊，离散数学里面的等价关系是等价类的划分，用来把一个大的集合划分成小集合，例如同余等价类。这个和C++的 equivalence 是同一个概念吗?

而map/set的排序要么是greater要么是less，不会同时判断a<b和b<a是否都成立，感觉并不是等价关系啊。

可能我的表述有些错误的地方，但是希望我把问题说清楚了。还请大侠指教。

------解决思路----------------------
参看《effictive STL》
------解决思路----------------------
可以参考std::rel_ops

引用

The phrase “equivalence of keys” means the equivalence relation imposed by the comparison and not the
operator== on keys. That is, two keys k1 and k2 are considered to be equivalent if for the comparison
object comp, comp(k1, k2) == false && comp(k2, k1) == false. For any two keys k1 and k2 in the
same container, calling comp(k1, k2) shall always return the same value.

------解决思路----------------------
楼上的解说是正解，请楼主仔细理解下
------解决思路----------------------
Each associative container is parameterized on Key and an ordering relation Compare that induces a strict
weak ordering (25.4) on elements of Key. In addition, map and multimap associate an arbitrary mapped type
T with the Key. The object of type Compare is called the comparison object of a container
------解决思路----------------------

引用:

Each associative container is parameterized on Key and an ordering relation Compare that induces a strict
weak ordering (25.4) on elements of Key. In addition, map and multimap associate an arbitrary mapped type
T with the Key. The object of type Compare is called the comparison object of a container

具体看25.4

STL联系关系容器为什么要定义等价关系? 明明是大小比较

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