Created
April 3, 2012 05:14
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russell's paradox in python
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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 |
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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) | |
# no sets contain themselves, so this is always False. | |
R = Set(lambda s: s not in s) | |
print R in R |
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