Calculus can be seen to have a special connection with the infinitely small, as differentiation is a limiting procedure as something goes to zero. Travelling on the graph from x to x + h, we rise a distance of f(x + h) – f(x) and run over a distance of h. This gets us the average slope over this distance, and we hone in closer and closer to the instantaneous slope at x as h becomes smaller and smaller.

But there is an analogue called finite calculus!

Consider what happens before we pass to the infinite world: we only can examine our function at individual steps. Perhaps something coarse like 1, 2, 3, 4, …; or perhaps something finer like 1, 1.05, 1.1, 1.15, …; but the step size is really not that important (it can be scaled), so we will assume that it is always 1.