Most people, shown that 0.999… with the nines running on forever is exactly 1, feel cheated, and the tidy proofs rarely help. A third is 0.333…, three thirds are 0.999…, and three thirds are also one. The trouble is the picture in the head: the nines being written, one more and one more, creeping toward 1 and never touching it, as if the number were a runner. But nobody is writing them. Every nine is already there, the whole endless row at once, and a number that isn’t on its way anywhere has nothing left to arrive at. Try to say how far apart the two are and you can’t name a distance; whatever small gap you offer, the nines have closed it a few places in. Two numbers with nothing between them are one number written twice.