Show ${\int}_0^{\infty}\delta(x+z)\delta(y-z)dz =\delta(y+x)$
It seems obvious, and I don't think we need a rigorous proof for this (statistical mechanics homework) but I want a rigorous proof of this anyway. I found something about 'nascent dirac delta' functions forming a semigroup under convolution on wikipedia, but I'm not good enough to use that, plus it's stated without proof. http://en.wikipedia.org/wiki/Dirac_delta_function#Semigroups