So, since we have shown the number of legs on a horse to be both even and odd, there must be infinitely many of them. A cat has nine tails. No cat has eight tails. A cat has one tail more than no cat. Therefore, a cat has nine tails.
All positive integers are equal.
We proceed by induction. Once, one of his students tried to get more helpful information by asking if there was another way to solve the problem. Norbert Wiener was renowned for his absent-mindedness. When he and his family moved from Cambridge to Newton his wife, knowing that he would be of absolutely no help, packed him off to MIT while she directed the move. Since she was certain that he would forget that they had moved and where they had moved to, she wrote down the new address on a piece of paper, and gave it to him.