There are many mathematical problems for which the solution is a function of some kind, and it is often whole real line has the useful property that sums and constant multiples of functions in the set are also in the s both possible and convenient to specify in advance the set of functions within which the solution is to be sought. For example, the solution to a first-order differential equation might be specified as being differentiable on the whole real line. The set of functions differentiable on the et. In fact, this set of functions has the structure of a vector space, where the “vectors” are functions.