2. General methods

2.1 Summation operations for comparison relations

We know that to study a sequence is to study the series of its differences and, similarly, to study a function (of class ${\mathcal{C}}^1$ ) is to study the integral of its derivative. Initially, we'll concentrate on the summation (or integration) of comparison relations. Formally, it suffices to deal with the second problem, since a discrete sum is nothing other than the integral of a piecewise continuous function. In practice, of course, the discrete sum is treated directly.