Imagine ourselves traveling from Maryland to Pennsylvania. What happens as we cross the Mason-Dixon line? Do we pass through a last point p in Maryland and a first point q in Pennsylvania?
Consider Aristotle's own riddle about motion: At the instant when an object stops moving, is it in motion or is it at rest?
Or consider the dilemma raised by Leonardo in his Notebooks: What is it that divides the atmosphere from the water? Is it air or is it water?
Or, again, consider Peirce's puzzle: What color is the line of demarcation between a black spot and its white background?
When exactly did the industrial revolution begin? When did it end? (Where did it take place?)
Extracted from http://plato.stanford.edu/entries/boundary/