diff --git a/src/sage/sets/set.py b/src/sage/sets/set.py
index 8c0668724d0..b76e6b064ef 100644
--- a/src/sage/sets/set.py
+++ b/src/sage/sets/set.py
@@ -693,7 +693,7 @@ def cardinality(self):
             except TypeError:
                 pass
 
-        raise NotImplementedError("computation of cardinality of %s not yet implemented" % self.__object)
+        return super().cardinality()
 
     def is_empty(self):
         """
@@ -1526,9 +1526,16 @@ def __init__(self, X, Y, category=None):
             sage: X = Set(IntegerRange(100)).intersection(Primes())
             sage: X.is_finite()
             True
+            sage: X.cardinality()
+            25
             sage: X.category()
             Category of finite enumerated sets
             sage: TestSuite(X).run()
+
+            sage: X = Set(Primes(), category=Sets()).intersection(Set(IntegerRange(200)))
+            sage: X.cardinality()
+            46
+            sage: TestSuite(X).run()
         """
         if category is None:
             category = Sets()
@@ -1538,27 +1545,6 @@ def __init__(self, X, Y, category=None):
             category = category.Enumerated()
         Set_object_binary.__init__(self, X, Y, "intersection", "\\cap", category=category)
 
-    def cardinality(self):
-        r"""
-        Return the cardinality of this set.
-
-        EXAMPLES::
-
-            sage: X = Set(IntegerRange(100)).intersection(Primes())
-            sage: X.cardinality()
-            25
-
-            sage: X = Set(Primes(), category=Sets()).intersection(Set(IntegerRange(200)))
-            sage: X.cardinality()
-            46
-        """
-        if self in Sets().Infinite():
-            return Infinity
-        if self in Sets().Finite():
-            from sage.rings.integer import Integer
-            return Integer(len(list(iter(self))))
-        return super().cardinality()
-
     def is_finite(self):
         r"""
         Return whether this set is finite.