On 7/11/2011 9:35 PM, MBALOVER 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 domain of the logarithm function is x > 0, so 0 is not in the domain of y = - log x. Hence any formula that uses logarithm becomes meaningless when its argument reaches that value, so, for example, the integral from -1 to 1 of log x is meaningless.
In contrast, with the Dirac delta function we end up attempting to make sense of what goes on at x = 0. The integral from -1 to 1 of this function is, unlike the logarithm, well-defined: it is 1. Since it is interesting for its unusual integral value, it is only used in the contexts where its definition as a function is invalid, unlike other classical functions.
-- Beware of bugs in the above code; I have only proved it correct, not tried it. -- Donald E. Knuth