Is the function 1/x continuous at 0?
  Brief development of the idea of the very important notion of continuity is given. Continuity is often confused with contiguity, "drawing the graph in one go," "no gaps," etc. The author argues in support of using correct notions of continuity as well as that of function, where continuity is not to be considered in vacuous situations, such as when the function does not exist. 
Radoslav M. Dimitric
math.GM