diff --git a/Lib/functools.py b/Lib/functools.py
index d450634..1062a45 100644
--- a/Lib/functools.py
+++ b/Lib/functools.py
@@ -68,17 +68,17 @@
 def total_ordering(cls):
     """Class decorator that fills in missing ordering methods"""
     convert = {
-        '__lt__': [('__gt__', lambda self, other: other < self),
-                   ('__le__', lambda self, other: not other < self),
+        '__lt__': [('__gt__', lambda self, other: not (self < other or self == other)),
+                   ('__le__', lambda self, other: self < other or self == other),
                    ('__ge__', lambda self, other: not self < other)],
-        '__le__': [('__ge__', lambda self, other: other <= self),
-                   ('__lt__', lambda self, other: not other <= self),
+        '__le__': [('__ge__', lambda self, other: not self <= other or self == other),
+                   ('__lt__', lambda self, other: self <= other and not self == other),
                    ('__gt__', lambda self, other: not self <= other)],
-        '__gt__': [('__lt__', lambda self, other: other > self),
-                   ('__ge__', lambda self, other: not other > self),
+        '__gt__': [('__lt__', lambda self, other: not (self > other or self == other)),
+                   ('__ge__', lambda self, other: self > other or self == other),
                    ('__le__', lambda self, other: not self > other)],
-        '__ge__': [('__le__', lambda self, other: other >= self),
-                   ('__gt__', lambda self, other: not other >= self),
+        '__ge__': [('__le__', lambda self, other: (not self >= other) or self == other),
+                   ('__gt__', lambda self, other: self >= other and not self == other),
                    ('__lt__', lambda self, other: not self >= other)]
     }
     # Find user-defined comparisons (not those inherited from object).