I'm new here and a new student in the university, I'm not accepting the idea how actually the "points" are not affecting the calculated quantity ; I mean:

lets assume that I have point a until point b and I want to calculate the distance, so it's b-a and if I wipe off point "b" so it will not included in the distance, but it's still the distance b-a , in other words I'm claiming that the distance between a and b is all the consecutive points between a and b (included a and b) ! ..so why if I wipe off the point b , the distance between a and b still b-a although I wiped off the point b ? what I claim that the distance must be b-a-(epsilon) and epsilon is because I wiped one point.

Another thing, why at integration, wiping points between the bounds that my integration is, will not affect the integral?

Maybe I miss understanding the definition of point and how it's going on math.

thanks!!