Steven D'Aprano wrote: > On Thu, 16 Jun 2005 21:21:50 +0300, Konstantin Veretennicov wrote: > > >>On 6/16/05, Vibha Tripathi <[EMAIL PROTECTED]> wrote: >> >>>I need sets as sets in mathematics: >> >>That's tough. First of all, mathematical sets can be infinite. It's >>just too much memory :) >>Software implementations can't fully match mathematical abstractions. > > > :-) > > But lists can be as long as you like, if you have enough memory.
But you never have enough memory to store, for example, a list of all the prime integers (not using a regular list, anyway). > So > can longs and strings. So I don't think the infinity issue is a big one. > > >>> sets of any unique type of objects including those >>>of dictionaries, I should then be able to do: >>>a_set.__contains__(a_dictionary) and things like that. > > > Standard Set Theory disallows various constructions, otherwise you get > paradoxes. > > For example, Russell's Paradox: the set S of all sets that are not an > element of themselves. Then S should be a set. If S is an element of > itself, then it belongs in set S. But if it is in set S, then it is an > element of itself and it is not an element of S. Contradiction. > > The price mathematicians pay to avoid paradoxes like that is that some > sets do not exist. For instance, there exists no universal set (the set > of all sets), no set of all cardinal numbers, etc. > > So even in mathematics, it is not true that sets can contain anything. See "Set Theory With a Universal Set" by T. Forster, which covers some set theories in which there *is* a set of all things, and in which Russell's paradox is avoided in other ways (such as by restricting the comprehension axioms). (Sorry for drifting offtopic, I happen to find non-standard set theories interesting and thought that some others here might too.) -- James -- http://mail.python.org/mailman/listinfo/python-list