diff --git a/gallery_dl/util.py b/gallery_dl/util.py
index 861ec7eb..e76ddf36 100644
--- a/gallery_dl/util.py
+++ b/gallery_dl/util.py
@@ -106,12 +106,12 @@ def identity(x):
     return x
 
 
-def true(_):
+def true(_, __=None):
     """Always returns True"""
     return True
 
 
-def false(_):
+def false(_, __=None):
     """Always returns False"""
     return False
 
@@ -540,10 +540,21 @@ class CustomNone():
     def __bool__():
         return False
 
+    __lt__ = true
+    __le__ = true
+    __eq__ = false
+    __ne__ = true
+    __gt__ = false
+    __ge__ = false
+
     @staticmethod
     def __len__():
         return 0
 
+    @staticmethod
+    def __hash__():
+        return 0
+
     @staticmethod
     def __format__(_):
         return "None"
diff --git a/test/test_util.py b/test/test_util.py
index 83b44b75..35e72473 100644
--- a/test/test_util.py
+++ b/test/test_util.py
@@ -745,6 +745,7 @@ def hash(value):
         self.assertEqual(repr(obj), repr(None))
         self.assertEqual(format(obj), str(None))
         self.assertEqual(format(obj, "%F"), str(None))
+
         self.assertIs(obj.attr, obj)
         self.assertIs(obj["key"], obj)
         self.assertIs(obj(), obj)
@@ -752,6 +753,17 @@ def hash(value):
         self.assertIs(obj(foo="bar"), obj)
         self.assertEqual(util.json_dumps(obj), "null")
 
+        self.assertLess(obj, "foo")
+        self.assertLessEqual(obj, None)
+        self.assertFalse(obj == obj)
+        self.assertTrue(obj != obj)
+        self.assertGreater(123, obj)
+        self.assertGreaterEqual(1.23, obj)
+
+        mapping = {}
+        mapping[obj] = 123
+        self.assertIn(obj, mapping)
+
         i = 0
         for _ in obj:
             i += 1