>>11623746You should have clarified in your image that the top half is an existing anti-physicist meme and the bottom half is your new and hot anti-mathematician meme in response to the top half.
Anyway, not touching the top half, but error terms are useful because there exist theorems that give us upper bounds on the error terms in certain problems. Maybe I want to use the approximationas many physicists and engineers do, and I want to know how far off I would be for . Well, I would use the Lagrange error bound and it would tell me how good the approximation is (very good, there's more variance in Earth's gravity at the surface).