  A new classification of real functions and other related real objects defined
within a compact interval is proposed. The scope of the classification includes
normal real functions and distributions in the sense of Schwartz, referred to
jointly as "generalized functions". This classification is defined in terms of
the behavior of these generalized functions under the action of a linear low
pass-filter, which can be understood as an integral operator acting in the
space of generalized functions. The classification criterion defines a class of
generalized functions which we will name "combed functions", leaving out a
complementary class of "ragged functions". While the classification as combed
functions leaves out many pathological objects, it includes in the same footing
such diverse objects as real analytic functions, the Dirac delta "function",
and its derivatives of arbitrarily high orders, as well as many others in
between these two extremes. We argue that the set of combed functions is
sufficient for all the needs of physics, as tools for the description of
nature. This includes the whole of classical physics and all the observable
quantities in quantum mechanics and quantum field theory. The focusing of
attention on this smaller set of generalized functions greatly simplifies the
mathematical arguments needed to deal with them.
