> 1/x also has a singularity, but as far as I'm aware, it's a perfectly normal function. No one integrates it over 0, but they do the delta function. > I reca

> 1/x also has a singularity, but as far as I'm aware, it's a perfectly normal function. No one integrates it over 0, but they do the delta function. > I recall that in my analysis class, they wanted to define the dirac delta as the limit of a sequence of functions. In my engineering courses, they often tried to make it a limit of the "rectangle" function. Consider a function that is 0 everywhere except between [-delta, delta], where its value is whatever is needed to make the area under this rectangle 1. Then let delta approach 0. This definition still fails using the standard limits/analysis that is taught (convergence problems, etc). In mathematics, the delta function needs the theory of distributions to "work".