Definition:Dirac Delta Function/Also defined as

Dirac Delta Function: Also defined as
It is commonplace to see the following definition or derivation for the Dirac delta function:
 * $\map \delta x := \begin {cases} \infty & : x = 0 \\ 0 & : x \ne 0 \end {cases}$

While this can be considered as acceptable in the context of certain branches of engineering or physics, its use is not endorsed on because of its lack of rigor.

For example, it is essential not only that the value of $\map \delta 0$ is not finite, but also that it is rigorously defined exactly how "not finite" it is.

That cannot be done without recourse to a definition using limits of some form.