Continuous singularity functions insight, extensions, and corrections

In spite of the proliferation of signals and system texts, authors have tended to avoid adequate treatments of continuous singularity functions. Furthermore, the limited treatments of singularity functions are not only incomplete, they often include erroneous concepts. Thus, the authors attempt to provide some insight to the nature of singularity functions, present a generalized extension of singularity function definitions, and correct a serious error in several signal and system texts. All topics are designed to supplement signal and system text instructions.