CDM Reason, Logic and Proofs

First, a classical example: the relationship between differentiable and continuous functions. It is clear that continuity is not enough for differentiability, a curve can have “corners” such as the absolute value function at 0. With a little bit of effort one can manufacture a continuous function that has countably many corners in the unit interval. E.g., one could have a kink at all positions 1/n, n a positive integer.