haael writes: > Could we add the idea of "negative" sets to Python? That means > sets that contain EVERYTHING EXCEPT certain elements.
This is usually called the "complement" of a set. Since (in set theory) there is no set of all sets, "absolute" complement is an unfounded concept. The idea of having a universe and defining "absolute complement" as complement relative to the universe is often adopted, but it has set-theoretic problems (the universe doesn't have a powerset, for one thing), and frequently you end up with a hierarchy of universes (categorists who try build category theory on set theory run into that a lot). Considering those points, this proposal seems very abstract. I think it's fun to think about, and maybe it has practical applications in constructing other sets. But a "set" that isn't iterable, and whose "in" is logically equivalent to "not in" its complement (which is a Python set!), doesn't seem directly useful in itself. I think this is one where you need to present both use cases and an implementation. Speaking of implementations and fun: > First, let's have a universal set that contains everything. > > assert element in set.UNIVERSAL For what values of "everything"? Python sets cannot contain all the objects of Python. Specifically, an element of a set must be hashable. Will that be true for your universal set? > The universal set is a superset of every other set. > > assert set.UNIVERSAL >= any_set Is it a superset of all iterables (however you want to define the transformation of iterables to sets, given the "hashability" issue)? > However REMOVING an element from the set puts it on "negative list". > > myset = set.UNIVERSAL Shouldn't this be "myset = copy(set.UNIVERSAL)"? You'd like it to be "myset = set(set.UNIVERSAL)", I guess, and that indeed would require adding set.UNIVERSAL to Python. > myset.remove(element) > assert element not in myset > > Intersection of a "negative set" with a normal set gives again a normal > set. Union of two negative sets, or a negative set with a normal set, > gives a negative set. > > The main issue: negative sets would not be iterable, but you can > intersect them with the desired subdomain and iterate over. > _______________________________________________ > Python-ideas mailing list -- python-ideas@python.org > To unsubscribe send an email to python-ideas-le...@python.org > https://mail.python.org/mailman3/lists/python-ideas.python.org/ > Message archived at > https://mail.python.org/archives/list/python-ideas@python.org/message/MY77JS226XWLV7FGTS4KRSWPI45VB64I/ > Code of Conduct: http://python.org/psf/codeofconduct/ > > _______________________________________________ Python-ideas mailing list -- python-ideas@python.org To unsubscribe send an email to python-ideas-le...@python.org https://mail.python.org/mailman3/lists/python-ideas.python.org/ Message archived at https://mail.python.org/archives/list/python-ideas@python.org/message/6X7OIK3BRHNZWLKFUMTQ3FJXGHRFIBU3/ Code of Conduct: http://python.org/psf/codeofconduct/
