Assume all sets of n horses are the same color Take a collection of n horses, they must be of the same color. Add another horse and take away a different one. Here we have a different set of n horses all of which are the same color.
All horses are the same color by induction.
Continuing, we can then show that all horses have an infinite number of legs. This is an odd number of legs for a horse to have. The only number that is both odd and even is infinity. Therefore, horses must have an infinite number of legs. To add weight to this argument we ponder whether a horse with a finite number of legs could exist.