Mathematically, it's not a function, it's a distribution. There are no infinitesimal intervals in the real numbers. This is merely a heuristic characterization. The Dirac delta is not a function in the traditional sense as no function defined on the real numbers has these properties. The Dirac delta function can be rigorously defined either as a distribution or as a measure. https://en.wikipedia.org/wiki/Dirac_delta_function#Definitions Surprised you didn't check on Wiki. It's perfectly obvious that it's not a mathematical function. The only question is the mathematical formalisms used to make it work out. I thought this was fairly well known. Then again, that's because I learned what I know about QM from the math side. Now I can see you put "function" in quotes so you're indicating you know this. But it doesn't take an infinite value on an infinitesimal interval. That's the physicist's intuition, but it's not the mathematical formalism.