...ne vale la pena.

«La semplicità è più difficile da raggiungere, rispetto alla complessità .C’è bisogno di lavorare duramente per cambiare il proprio modo di pensare, renderlo pulito e lineare e dunque semplice. Ma ne vale la pena. Perché quando raggiungi quel modo di pensare, puoi muovere le montagne».

Steve Jobs

Introductio in analysin infinitorum

Bach - Bernoulli

to the limit...

Darboux Functions

A real valued function f defined on an interval I is said to nave the intermediate value property if whenever a and b are in I, and y is any number between f (a) and f(b), there is a number x between a and b such that f(x) = y. This property was believed, by some 19th century mathematicians, to be equivalent to the propertyof continuity. In 1875, Darboux showed that this belief was not justified. He proved that every derivative has the intermediate value property and he gave examples of some rather badly discontinuous derivatives. (We now know that a function having the intermediate value property can be discontinuous everywhere, and, in fact, be nonmeasurable on every set having positive measure.) Because of Darboux's work on the subject, one now usually calls a function having the intermediate value property a Darboux function.

Now, every derivative has the Darboux property. The same is true of every function belonging to any of several classes of functions which are related to the class of derivatives.

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