Business donuts are strictly ornamental

Last time I was down at U of T, their career center had a book posted in its window, entitled Don't take the last donut: New rules of business etiquette.

Let's take the title advice seriously: as a matter of business etiquette, don't take the last donut. Why? Obviously, because it's impolite to deprive someone else of the option to have a donut.

Now assume that everyone is polite, and suppose there are two donuts left. What if you take the second-to-last donut? It's impolite for anyone else to take the last donut, so since everyone is polite (by assumption), your action deprives everyone else of a donut. Thus, it must be as impolite to take the second-to-last donut as it is to take the last one. We can make a similar case for the third-to-last and fourth-to-last donut.

Indeed, by the same argument, we can construct an inductive case: assuming it is impolite to take the nth-to-last donut (for any n >= 1), and there are (n+1) donuts available, then it must be equally impolite to take the (n+1)th-to-last donut, because nobody can (politely) take a subsequent donut.

Thus, by induction, for any integer n > 0, it is impolite to take the nth-to-last donut. Thus, business donuts are strictly ornamental and it is impolite to ever eat them. QED.