View source for Fallacious proof/all horses are the same color

Our base case is not the appropriate base case: if one could show that every pair of horses has the same color (the result for <math>n = 2</math>), the fact that all horses have the same color would follow.  Unfortunately, the case <math>n = 2</math> does not follow from the case <math>n = 1</math>. The first horse is the same color as itself, and so is the second horse, but there is no overlap.