@Arjun I can understand why people wonder why I spent so much effort answering this question. The reason is that this question provides a great example of a problem we face in mathematics education. The fact that the question was posted over five years ago, but only recently answered with a valid proof, suggests to me that a better understanding of elementary arithmetic is needed. I think that a better understanding has implications for the way elementary arithmetic is taught. I find it a hard sell, though. Most people think that elementary arithmetic is ... well...elementary. — Peter Baum 27 mins ago