This is called proof by induction. There is an intuitive path to understand it: Consider the set of the natural numbers; it contains 0 (zero) and for any K whic

This is called proof by induction. There is an intuitive path to understand it: Consider the set of the natural numbers; it contains 0 (zero) and for any K which belongs to this set, its successor (K + 1) also does. It is clear that if a property if valid for 0 and, in the case it is valid for a K which is not 0 implies it is also valid for K + 1, then such property is valid for all natural numbers.