Detail the semantics more, following python-ideas questions

pep-0428.txt

@@ -165,10 +165,32 @@ are tied by backwards compatibility to confusing or plain wrong behaviour
 (for example, the fact that ``os.path.abspath()`` simplifies ".." path
 components without resolving symlinks first).
 
-Also, using classes instead of plain strings helps make system-dependent
-behaviours natural.  For example, comparing and ordering Windows path
-objects is case-insensitive, and path separators are automatically converted
-to the platform default.
+
+Comparisons
+-----------
+
+Paths of the same flavour are comparable and orderable, whether pure or not::
+
+    >>> PurePosixPath('a') == PurePosixPath('b')
+    False
+    >>> PurePosixPath('a') < PurePosixPath('b')
+    True
+    >>> PurePosixPath('a') == PosixPath('a')
+    True
+
+Comparing and ordering Windows path objects is case-insensitive::
+
+    >>> PureNTPath('a') == PureNTPath('A')
+    True
+
+Paths of different flavours always compare unequal, and cannot be ordered::
+
+    >>> PurePosixPath('a') == PureNTPath('a')
+    False
+    >>> PurePosixPath('a') < PureNTPath('a')
+    Traceback (most recent call last):
+      File "<stdin>", line 1, in <module>
+    TypeError: unorderable types: PurePosixPath() < PureNTPath()
 
 
 Useful notations
@@ -222,8 +244,8 @@ First a couple of conventions:
   "anchored" is the same as "absolute".
 
 
-Construction and joining
-------------------------
+Construction
+------------
 
 We will present construction and joining together since they expose
 similar semantics.
@@ -256,12 +278,29 @@ However, with Windows paths, the drive is retained as necessary::
     >>> PureNTPath('c:/foo', 'd:')
     PureNTPath('d:')
 
+Also, path separators are normalized to the platform default::
+
+    >>> PureNTPath('a/b') == PureNTPath('a\\b')
+    True
+
+Extraneous path separators and ``"."`` components are eliminated, but not
+``".."`` components::
+
+    >>> PurePosixPath('a//b/./c/')
+    PurePosixPath('a/b/c')
+    >>> PurePosixPath('a/../b')
+    PurePosixPath('a/../b')
+
 Calling the constructor without any argument creates a path object pointing
 to the logical "current directory"::
 
     >>> PurePosixPath()
     PurePosixPath('.')
 
+
+Joining
+-------
+
 A path can be joined with another using the ``__getitem__`` operator::
 
     >>> p = PurePosixPath('foo')