$$\infty + 1 = \infty$$ subtract infinity from both sides. $$1=0$$
At first I thought, duh, $\infty \neq \infty+1$, but, now, I'm just more confused because my brother rephrased it in terms of geometry, and it seems to hold there i.e., if you have a ray of infinite (unbounded) length, and then you start a parallel ray one unit behind it, how long is the new ray? I want to say infinite, but then, if you subtract the length of the ray beside it, then the result is the same as in the first problem.
Is there any way someone could explain why this doesn't work?