It's been a long time since I've done any physics and there is absolutely no rigour here, but the (extremely useful) Dirac delta function comes to mind. You can

It's been a long time since I've done any physics and there is absolutely no rigour here, but the (extremely useful) Dirac delta function comes to mind. You can think of it as being infinitely tall and infinitely thin, but with unit area. If you tried to divide the "area" (1) by the "width" (0), you'd get the height (infinity).