Editing Piecewise linear function (section)

==Definition==
A piecewise linear function is a function defined on a (possibly unbounded) [[Interval (mathematics)|interval]] of [[real number]]s, such that there is a collection of intervals on each of which the function is an [[affine transformation|affine function]]. (Thus "piecewise linear" is actually defined to mean "piecewise [[affine function|affine]]".) If the domain of the function is [[compact space|compact]], there needs to be a finite collection of such intervals; if the domain is not compact, it may either be required to be finite or to be [[Locally finite collection|locally finite]] in the reals.