Sequences

The process of abstraction involves finding a description of a particular object that contains just enough information—not too much. The mathematical data types that we have introduced so far allow us to record collections of objects as sets, and the relationships between them as relations and functions. Sometimes it is important to place these objects in some sort of order, they may be sorted according to some key for example. In order to describe a collection of objects whose order is important, we introduce a new data type: the sequence¹. In fact, we already have enough notation to describe ordered sets, so we shall build on this.