>> >> The Dirac delta function does not assign a real number to zero, >> >> and is thus not a true function. >> >> >Thanks Gerry. But I am still confused. I think at x =3D 0, delta(x) = >> >infinity. >> >> That's one way of looking at it -- in fact it's the one that I was >> taught while studying electical engineering. However, look more >> carefully at what was said: "... does not assign a real number to >> zero ...". >> >> There is no real number called "infinity". > >Quite. > >You could try to think of delta as a function >from the reals to the extended reals, the extended >reals being "the reals union infinity", but that >won't help you to understand why >integral from minus infinity to infinity of f(x) delta(x) dx >is f(0).
It's been a long time since I studied this, but isn't that true for the integral from minus epsilon to epsilon (for any positive epsilon), as well?
-- Michael F. Stemper #include <Standard_Disclaimer> Life's too important to take seriously.