Zeno might appreciate this (where “appreciate” is used in the technical sense of “bang head against wall on account of”). Via Isabel comes Eric Schechter’s page of Common Errors in College Math. If you survived calculus, read through it and congratulate yourself on all the mistakes you don’t make anymore!

(See how optimistic I am?)

Schechter provides one of the most inspiring examples of getting the right answer through the wrong method that I’ve ever seen. The problem is to evaluate the following definite integral:

$$\int_0^{2\pi} \cos x\, dx.$$

This is how our student started:

$$\int_0^{2\pi} \cos x\, dx = \left.\frac{\sin x}{x}\right|_0^{2\pi} = \frac{\sin 2\pi}{2\pi} – \frac{\sin 0}{0}.$$

But wait, there’s more!

$$\frac{\sin 2\pi}{2\pi} – \frac{\sin 0}{0} = \sin – \sin = 0.$$

And they say we can’t eliminate sin from the world.