walterbyrd writes: "Here's an absolutely brilliant idea from Apple: imagine if you had a bunch of different gadgets, and imagine if they could all somehow be powered by batteries that were rechargeable and all interchangeable with one another. How awesome would that be? Super awesome! If only we'd thought of it a long time ago."
We warn the reader in advance that the proof presented here depends on a
clever but highly unmotivated trick.
-- Howard Anton, "Elementary Linear Algebra"