N is closed in R

Note-1: Post is not about Metric Space discussions, but about my experience with the 10XX batch as a tutor  for ST-1 (Mathematical Analysis).

Note-2: Reason for the title, is around the end of post. you may directly skip to that part.

Note-3: This post is going to be pretty long and boring, so can be skipped.

I was assigned the Tutorials for this course in July. I was informed that Dr. A. D. Joshi (retd. Prof. from Dept of Mathematics) is taking the course. I was little unsure, as in how will it be to assist a total stranger, who doesn't actually belongs to our department. But first hand interaction went quite well. I heard him discussing countable sets with the students.That very moment I liked his way of looking at analysis, which was not completely theoretical.

Tutorials started. Though I had an "O" in ST-1, to be frank I am not very good in it. But with the help of Akanksha and few books and some hard work, I got  confidence. At the end of semester I feel I have improved a lot in the subject.

In first lecture itself I announced that its not at all compulsory to attend the sessions(scheduled once a week). Initially attendance was not good, not bad kind. That encouraged me. But slowly it decayed like anything. You can imagine the pattern.. 48, 14, 27, 43, 16, 20, 25, 21, 20, 4, 7, 6, 10 ... thats how it was. Coming down to 4 in class of 50 was a real shock to me. I kept on wondering whats wrong with me. I discussed the issue with people who are experienced in the field. But somehow, there was no point in changing the strategy. I went on with it. I tried asking those 4 who were almost regular, that they can tell me the actual problem, I won't mind. But there reaction was, they like mine better than the tutorials for other 2 subjects. So, I left it to time. But I was disheartened. My love and zeal for teaching these topics, was suppressed by their non-response. I no more felt like taking efforts.

Just a week before 2nd internals, few of them got really scared, after looking at their 1st internal scores. They requested for extra sessions. That week I worked some 4 hours with them. And after looking at 2nd internal scores, I smiled, because it was worth those 2-3 extra sessions. And I got some of my lost enthusiasm back.

Why I am writing this today?  Today was the end-term exam. First person I saw was a girl, who was upset on how difficult the question paper was. How could Sir do this with them, with such a difficult paper. I found it okay kind. Though it was not easy, there was nothing impossible there. Then came another, who was again upset. This girl was regular after 2nd internals, unlike the first one. Her reaction was "Why didn't you took the complete course. If you would have been there, it  must have been lot better. Tutorial helped me a lot to help the concepts, but the lectures were helpless".

My point, which I could not actually tell them was... Why don't you understand, the course has to be blend of the two. And by what I know and felt about ADJ, he is amazing. Its just that his way is little different and diagrammatic. But he cannot be blamed for your poor performance. It is you who are responsible for that.

Then comes the reason for the statement in tutorial which is revolving in mind. Both the girls proved it in the paper(as they told me). No wonder. But how they did was wonderful. They were somehow able to show, that all the limit points of set of  Natural nos. lie in R. But I was not able to understand how come they don't realize that Naturals don't have limit points.

Anyways, to my relief, after few mins two guys came who have proved it in the right manner (i.e. since N doesn't have limit point it has to be closed), and they were quite confident and relaxed about it, which made me feel better.

I don't have any regrets. Because it helped me to learn and evolve in the subject over the time. It might have been a better experience with the participation. But that taught me many new aspects of teaching.

PS: So many times during these 4 months I felt an urge to lighten myself with the burden of feelings I had about the experience. But I never could. May be because that was not the right time. And it is now, because the experience is complete now.

Post PS: Check out this tone-matrix. Just put your speakers on, and start clicking. I am sure you will enjoy.