An inductive definition is defined by its properties. The definition itself may not tell us how to construct any examples. However, it will naturally lead to the general construction once we endow the definition with a physical meaning. A physical meaning of scalar product: The kinetic energy in terms of generalized coordinates [Gol, p.326, l.2]. General method of reproduction:
Differentiation is the inverse of integration. More precisely, its key idea is to take the infinitesimal average [Kap, p.240, (4.49) & p.240, l.-6]. We should not be distracted from this main concern [Kap, p.240, l.-1] by any special type of approach, say, using an abstract measure [Ru2, p.164, Definition 8.3] and a sequence of open balls [Ru2, p.163, l.-2].