note35 · July 2, 2018 12:39 · Apr 3, 2012 · Apr 3, 2012
diff --git a/sets.py b/sets.py
@@ -8,7 +8,6 @@ def __init__(self, predicate):
     def __contains__(self, obj):
         return obj is not self and self.predicate(obj)
 
-# we can do this just fine, though -- it's always False because no sets contain
-# themselves.
+# no sets contain themselves, so this is always False.
 R = Set(lambda s: s not in s)
 print R in R
diff --git a/naive_sets.py b/naive_sets.py
@@ -0,0 +1,14 @@
+class Set(object):
+    """Sets can contain anything, including themselves. This leads to
+    paradoxical behavior: given R, the set of all sets that don't contain
+    themselves, does R contain R? Here this becomes an infinite recursion.
+    """
+    def __init__(self, predicate):
+        self.predicate = predicate
+
+    def __contains__(self, obj):
+        return self.predicate(obj)
+
+# We hit the recursion limit with this:
+R = Set(lambda s: s not in s)
+print R in R
diff --git a/sets.py b/sets.py
@@ -0,0 +1,14 @@
+class Set(object):
+    """If we add another stipulation -- no sets contain themselves -- we
+    exorcise this particular paradox.
+    """
+    def __init__(self, predicate):
+        self.predicate = predicate
+
+    def __contains__(self, obj):
+        return obj is not self and self.predicate(obj)
+
+# we can do this just fine, though -- it's always False because no sets contain
+# themselves.
+R = Set(lambda s: s not in s)
+print R in R
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