diff --git a/Doc/library/unittest.rst b/Doc/library/unittest.rst
index 845bf0a2958..0c00a261c44 100644
--- a/Doc/library/unittest.rst
+++ b/Doc/library/unittest.rst
@@ -1000,7 +1000,7 @@ Test cases
       like the :func:`round` function) and not *significant digits*.
 
       If *delta* is supplied instead of *places* then the difference
-      between *first* and *second* must be less (or more) than *delta*.
+      between *first* and *second* must be less or equal to (or greater than) *delta*.
 
       Supplying both *delta* and *places* raises a ``TypeError``.
 
diff --git a/Lib/unittest/test/test_assertions.py b/Lib/unittest/test/test_assertions.py
index d43fe5a601b..7931cadaf3d 100644
--- a/Lib/unittest/test/test_assertions.py
+++ b/Lib/unittest/test/test_assertions.py
@@ -34,6 +34,10 @@ class Test_Assertions(unittest.TestCase):
         self.assertNotAlmostEqual(1.1, 1.0, delta=0.05)
         self.assertNotAlmostEqual(1.0, 1.1, delta=0.05)
 
+        self.assertAlmostEqual(1.0, 1.0, delta=0.5)
+        self.assertRaises(self.failureException, self.assertNotAlmostEqual,
+                          1.0, 1.0, delta=0.5)
+
         self.assertRaises(self.failureException, self.assertAlmostEqual,
                           1.1, 1.0, delta=0.05)
         self.assertRaises(self.failureException, self.assertNotAlmostEqual,