Sarah Sarah	Posted on Tuesday, 10 February, 2004 - 12:33 pm: What does this symbol $\subset$ mean without the line underneath? It appears in the Mathworld entry Axiom of the Power Set
Julian Pulman	Posted on Tuesday, 10 February, 2004 - 12:44 pm: If , then A is a proper subset of B; in this case A CANNOT be equal to B.
Tim Bellis	Posted on Tuesday, 10 February, 2004 - 01:54 pm: I'm not sure how standard that is; I've seen either notation used by lecturers to mean that A can be equal to B. I think it's a matter of preference which symbol you use (or whether you follow Julian's convention), but if there's a danger of ambiguity it's a good idea to make sure your reader knows what you mean. Tim
Dan Goodman	Posted on Tuesday, 10 February, 2004 - 02:51 pm: ... but in the Mathworld definition you linked to, it just means ordinary subset, i.e. it allows for A to be equal to B. As Tim says, it's ambiguous but I think nowadays most people don't use it to mean "proper subset". There's a symbol which looks like the subset symbol with a "not equal to" symbol underneath which is used unambiguously for proper subset. Let's see if it works: or And in really old logic textbooks means p implies q (you can remember it because if p implies q then the content of q is contained within the content of p, p means more than q).
Dan Goodman	Posted on Tuesday, 10 February, 2004 - 02:53 pm: Oh, and here are two more variants: and
Kerwin Hui	Posted on Tuesday, 10 February, 2004 - 07:16 pm: Moral of the story: if you mean a proper subset, then use or . If you just mean a subset (could be the whole set), then use or . Kerwin