On 2011-07-12, MBALOVER <email@example.com> wrote: > Thanks Gerry. But I am still confused. I think at x = 0, delta(x) = > infinity. If so, y = -log(0) = + infinity too. Is y = - log(x) Not a > true function?
The expression "-log(x)" can define a true function from R^+ to R, but does not define a function from R to R.
There are a number of ways to define the Dirac delta "function" (more strictly, a distribution), but none of them involve "delta(x) = infinity". Some distributions correspond to real functions, some do not. The delta distribution is one of those that does not.