A point on a line is a boundery that seperate it into two parts at that point. As we assume that a point has measure 0,it does'nt affect to the substance in ordinary sence. But in set theory, it is considered as a part of substance. Therefore we can take out this boundery ,and leave void. We can point out a point, but cannot remove it, that is my view about a line. Objects that discreet points are removed from compact set are important concept in real analysis and are very useful. For example, open set,dense set... The treatment to remove a point may be translated the treatment to ignore this point. The treatment that I want to inhibit is to build objects which are constracted from members which looks like being connected intimately in the condition being seperated from each other like Vitali set. My wish is to leave real analysis intact as far as possible ,and avoid these odd objects.
