Hi Jyotsna: I read about your problem yesterday, but since I wasn't a member of this group, I had to apply for it, and wait for a day to write a reply. So, even if it is late, here is my suggestion. == Take an open covering of set (0,infinity) , in this case A=countable union of (n-epsilon,n+1+epsilon), where those epsilons make sure that you got the whole damn thing,[0,infinity) covered. Now, I hope you know what I meant by countable union, this is n=0 to infinity, just in case. In this case, as you can see [0,infinity) is in A.Now, suppose n doesn't go to infinity but some finite number N. Can you say the same thing: that this ugly sucker (i.e. [0,infinity) set) also belongs to A? No. Which means there is no finite subcovering of this open covering. == I hope it helps. I am trying to be chivalrous, by helping out a girl in need. If somehow you turn out to be a boy, then, it will be quite a disappointment for me. Anyway:-)