Commits on Oct 5, 2023

1. docs: Correct terminology in std::cmp …

   Some clarifications regarding used (mathematical) terminology:
   
   * Avoid using the terms "total equality" and "partial equality" in favor
     of "equivalence relation" and "partial equivalence relation", which
     are well-defined and unambiguous.
   * Clarify that `Ordering` is an ordering between two values (and not an
     order in the mathematical sense).
   * Avoid saying that `PartialEq` and `Eq` are "equality comparisons"
     because the terminology "equality comparison" could be misleading:
     it's possible to implement `PartialEq` and `Eq` for other (partial)
     equivalence relations, in particular for relations where `a == b` for
     some `a` and `b` even when `a` and `b` are not the same value.
   * Added a section "Strict and non-strict partial orders" to document
     that the `<=` and `>=` operators do not correspond to non-strict
     partial orders.
   * Corrected section "Corollaries" in documenation of Ord in regard to
     `<` only describing a strict total order in cases where `==` conforms
     to mathematical equality.
   
   Made documentation easier to understand:
   
   * Explicitly state at the beginning of `PartialEq`'s documentation
     comment that implementing the trait will provide the `==` and `!=`
     operators.
   * Added an easier to understand rule when to implement `Eq` in addition
     to `PartialEq`: "if it’s guaranteed that `PartialEq::eq(a, a)` always
     returns `true`."
   * Explicitly mention in documentation of `Eq` that the properties
     "symmetric" and "transitive" are already required by `PartialEq`.

   

   JanBeh committed Oct 5, 2023
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