#mathematics It has never been easy to teach the mathematical definitions of

**limits**and**continuity**. How to visualize the passing to the limit hidden behind the apparently "static" definition? Every year I try to illustrate this definition in an intuitive and geometric way ...View 4 previous comments

- Interesting way of doing it. I've been struggling to find a way to truly appreciate the logical step to the rules we use to determine differentiation of one function. I nees to keep studying, but I'm sure that a graphical prepresentation is the key.Sep 17, 2015
- +philippe roux +Rene Grothmann I changed the point of view and was looking at the line as an physical object. In this case you get by a similar limiting process a wave equation ;-).Sep 18, 2015
- Ah well: pointwise continuity, uniform continuity, Cauchy continuity, Hölderlin continuity, Lipschitz continuity: only half a dozen notions to explain and tell apart, easy peasy ;)Sep 18, 2015
- I think you missed a 0 < in the first inequalitySep 19, 2015
- +Rodrigo Appendino the definition of limits with the condition 0<|x-x_0|<eta is different from the definition I illustrated here (it is called "blunt limit" in French). Each definition as its advantages and disadvantages :

1) The advantage of the "|x-x_0|<eta" definition is that the limit f(g(x)) = f(limit g) which is false with the "0<|x-x_0|<eta" definition !!!

2) The advantage of the "0<|x-x_0|<eta" definition is that limit of the characteristic function 1_{0}(x) when x->0 is 1 ... which is false with the "|x-x_0|<eta" definitionSep 21, 2015 - Living and learningSep 22, 2015