During the last sixty years a new concept has been developing in mathematics which I will call the ability to say "no." Although it may date farther back, for present purposes we may regard it as starting in the I88O'S with the work of Heaviside 1 on his operational calculus. This was the subject of much controversy, regrettably.
About I916 Bromwich 2 and Wagner 8 showed that results similar to Heaviside's could be obtained by more nearly "standard" mathematical methods. Interest in these alternative methods grew and starting around I925 a number of books 4 on the subject of these and other alternative methods were published. It seems reasonable to assume that if all these different methods give the same results, there must be some unifying principle which brings this about.
In comparing these various methods, it becomes apparent that they are all making use of a new concept in mathematics which is the ability to say "no." This ability enables the discontinuous functions encountered in the solution of many problems to be represented by a single expression, instead of two or more, without any ambiguity. This simplifies and shortens mathematical processes.
Before discussing this concept in more detail, it may be well to reflect for a moment on how similar concepts have often waited for a long time before being admitted into mathematics. First only integers were used and centuries elapsed before fractions were introduced. The negative numbers were quite a problem but they finally found acceptance. The imaginary had similar difficulties and then came the complex numbers. Most people are acquainted with the fact that