## Down the rabbit hole

The following has been a rather interesting journey – from a test question which seemed fine, to a subtlety which seemed easy, to a discussion with a number of different mathematicians about the nature of distributions, measure theory and regularisation. I will try and make it as clear as possible in the post below. Note, as mentioned in the comments, we have actually only found the solution to this problem for a constrained range of x, and not x . I didn’t want to complicate things any more than necessary here for first year students, but the comments are very important too.

In a recent class test, there was a question, written by me, which was not quite the question that I wanted to ask. It turns out that it does have an answer, but it’s not an answer that can yet be found by the means at the class’s disposal.…