Infinitesimal Worms
A discontinuity paradox
I've always loved the joke where you bite into an apple and find a worm but then you have to be relieved about it because that is still better than biting into an apple and finding half a worm. Extending this further, you would prefer half a worm in your apple than a quarter of a worm. So on and so forth, until it means that the worst case scenario is when you don't find any worms in your apple.
What is worse than finding $1/n$ of a worm in your apple? Finding $1/n^2$ of a worm your apple. Hilariously, this works for cases where $n\in\mathbb{R}^+$ except that the grammar doesn't hold up. Example: for $n=1/7,$ what is worse than finding 7 worms in your apple? Finding 49 worms in your apple.