This was an old proof that was up on my old blog, but since I’m no longer posting to that, I’m reposting it here for posterity. Also, rewriting the equations in LaTeX, now that I have installed a plugin for that.
I present a simple mathematical device to prove that tests improve our understanding of code. It does not really matter if this is code written by the test author himself or is legacy. To do this, some simplification of the situation is necessary.