Recent content by jasonchen2002

That's the main trouble, I can't seem to describe the answer... If x is in A \ B_n for all n, then x is in a set containing A "minus" B_n for all n, but n goes from 1 to infinity, that's the whole set B_n (union), so x is in A "minus" the union of B_n? As for the other way around, take y \in A...

Right! I get it now. If I set S to (Q /\ [0,1]) \/ [2,3], then int S = (2,3), cl S = [0,1], int (cl S) = (0,1), and cl (int S) = [2,3]?

Homework Statement Given a set A \in R^m, B_n \in R^m for n \in N, show that A \ Union {from n = 1 to inf} B_n = Intersection {from n = 1 to inf} (A \ B_n} Homework Equations Same equation as above The Attempt at a Solution I think I have a solution in mind, but I wanted to...

Nice! That's one step closer to the answer, but somehow I can't distinguish the difference between int S and cl(int S)... Say, if I union Q /\ [0, 1] with a set {any number than 0 and 1}, would that work? So would it be that the interior is the set {..}, and the closure of the interior is R...

Thank you for your hint, I just wonder if it's possible to continue to work on the solution along the way while getting feedbacks from forum members... So I just need to restrict S to some smaller/specific numbers? Something like 0 to 1? And about the additional requirements for the set, does...

Homework Statement Construct a set S in R such that - S - interior of S - Closure of S - Closure of the interior of S - Interior of the closure of S Are all distinct from each other. Homework Equations I don't think there should be any. The Attempt at a Solution I 'm...