I seem to recall that part of Heisenberg's theory is that there is always room for improvement in measuring, and due to that room for improvement, due to our increasing precision,no measurement can ever be seen as absolutely correct. Wouldn't this be catered for by the limits in calculus? Wouldn't limits ensure that our measurements are essentially correct?
Heisenberg's uncertainty principle has nothing to do with our capacity to measure things. It is a fundamental limit on how well certain pairs of quantities can be defined. For example, it says that position and momentum are related in such a way that if you know one of them very accurately, you cannot know the other to great accuracy - no matter how good your measuring equipment is. Position and momentum are quantities which become "fuzzy" at the quantum level.
QED Richard Feynman's book "Q.E.D." is very insightful! You should read it. everyone should! Heisenbergs uncertainty principle will suddenly become the most logical phenomenon imaginable. Hmmm sort of.