#16676: Cardinality of infinite sets loops forever
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Reporter: defeo | Owner:
Type: defect | Status: new
Priority: major | Milestone: sage-6.3
Component: combinatorics | Resolution:
Keywords: sets infinite_loop | Merged in:
Authors: | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: | Stopgaps:
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Comment (by defeo):
Looping forever is always a bug in my opinion. The class
`Set_object_difference` knows in advance that the loop is not going to
stop when the first set is infinite, thus it could avoid the computation.
This only solves the first layer of the problem, though.
Obviously the problem is undecidable. A properly designed system should
only start the enumeration when it **knows** the set is finite. This is
best implemented with three-way logic, a topic that resurfaces often in
discussion threads.
The semi-decidable algorithm could still be run by a call to
`is_finite(try_hard=True)`, then `Set_object_difference` could be smart
and run it only when `self.__X.is_finite(try_hard=True)` returns true.
However this would require a thorough redesign of the `Set` API, which I
do not have time to start right now. I was merely reporting the bug for
reference.
By the way, the fix you suggest would clash on the following bug of
`is_finite()`:
{{{
sage: Set(ZZ).difference(Set()).is_finite()
...
RuntimeError: maximum recursion depth exceeded while calling a Python
object
}}}
This is a different problem and an easy fix, though, as long as we agree
that `False` means "I don't know".
--
Ticket URL: <http://trac.sagemath.org/ticket/16676#comment:2>
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