Editing Discrete mathematics (section)

==== Calculus of finite differences, discrete analysis, and discrete calculus ====
In [[discrete calculus]] and the [[calculus of finite differences]], a [[function (mathematics)|function]] defined on an interval of the [[integer]]s is usually called a [[sequence]]. A sequence could be a finite sequence from a data source or an infinite sequence from a [[discrete dynamical system]]. Such a discrete function could be defined explicitly by a list (if its domain is finite), or by a formula for its general term, or it could be given implicitly by a [[recurrence relation]] or [[difference equation]]. Difference equations are similar to [[differential equation]]s, but replace [[derivative|differentiation]] by taking the difference between adjacent terms; they can be used to approximate differential equations or (more often) studied in their own right. Many questions and methods concerning differential equations have counterparts for difference equations. For instance, where there are [[integral transforms]] in [[harmonic analysis]] for studying continuous functions or analogue signals, there are [[discrete transform]]s for discrete functions or digital signals. As well as [[discrete metric space]]s, there are more general [[discrete topological space]]s, [[finite metric space]]s, [[finite topological space]]s.

The [[time scale calculus]] is a unification of the theory of [[difference equations]] with that of [[differential equations]], which has applications to fields requiring simultaneous modelling of discrete and continuous data. Another way of modeling such a situation is the notion of [[hybrid system|hybrid dynamical system]]s.