I was under the impression that we were talking about mathematics and not physical reality. In mathematics, cos/sin are just functions cos:R -> R and sin:R ->

I was under the impression that we were talking about mathematics and not physical reality. In mathematics, cos/sin are just functions cos:R -> R and sin:R -> R. As far as functions go, Dirac delta is kind of a fiction because we don't have a function δ: R -> R. That's why I think that your initial characterization was correct. Of course if we define it with distribution or measure then we don't have this issue. > Maybe this way of thinking about the dirac delta in obvious to everyone, but to me it was a major breakthrough because I couldn't imagine how something infinitely tall and infinitely narrow could model anything in the real world. By the way, if you're looking for intuition on the Dirac delta I think a good way to think of it is just the identity element under convolution. Equivalently, you can think of it as a thing whose Fourier transform is 1.