Hi, This might be a trivial question, but I'll ask it anyway. Why is this not an open interval? Let a, b be two elements in X, such that a < b. Then, every real number c satisfying the order relation a < c < b is necessarily in (a, b) and hence in X. Hence X is an interval. Since X is equivalent to the interval (0, [itex]\infty[/itex]), I assumed it is also an open interval. Does the definition of an open interval only apply to intervals with finite end points? I thought otherwise: http://en.wikipedia.org/wiki/Interval_(mathematics)#Infinite_endpoints. Thanks in advance.