Least and the greatest fixed points

It was one of the early days in first sem in the college when I missed a few parts of the lecture as I was dozing. I went up to the nimble girl who seemed to have an agile mind that was pretty evident from her questions in the class. She attentively put down all class notes too. I thought I would borrow her class notes for a day or two. "Do write down your mobile number", I found these words somewhat unexpected as they pierced through my ears. I was certainly not going to run away with the class notes!

Well, along the years as I witnessed similar incidents, I was more and more convinced that there is nothing wrong in it. It is just that some people are more careful, particularly the members from the fairer sex. We have two very different and distinct psychologies. Some of us tend to trust in people around us and continue to do so until we find that one is unworthy of it. I fall in this group and I believe that this group shows more optimism in day to day activities than the other group which considers that one can be trusted only through good relationships that last over long period of time. The latter reflects a more conservative approach. On the other hand, I strongly believe that people around me will be very much similar in a broad sense and share a similar background and there is no reason why I should not believe in them.

This sounds to me very similar to the way we calculate the greatest and the least fixed points. Both the least and greatest fixed points are the intended solutions but for the former we start with a null set and keep on adding elements to it until we reach the fixed point. While calculating the greatest fixed point, we start with the universal set and eliminate elements until we obtain the fixed point. Both lead to solutions but the former leaves out some elements that could have been part of our solution. So we fail to get to know a few people who could have been closer to us if we initialize the basket of our trustworthy people with no one. The old may argue that it is just my youth which ventures and time might change things as I move along.