The horse paradox is an apparent paradox which arises from the following supposed demonstration, using mathematical induction, of the statement All horses are the same colour: As the basis case, note that in a set containing a single horse, all horses are clearly the same colour. Now assume the truth of the statement for all sets of at most n horses. Let there be n + 1 horses in a set. Remove the first horse to get a set of n horses. By the induction hypothesis, all horses in this set are the same colour.