86b031b734
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`. |
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