Fundamental definitions do not arise at the start but at the end of the exploration, because in order to define a thing you must know what it is and what it is good for. 

                                                     Hans Freudenthal, Developments in Mathematical Education 

 Give me a fruitful error anytime, full of seeds, bursting with its own corrections. You can keep your sterile truth for yourself. 

                                                   Vilfredo Pareto