Mathematical Induction

Claim:All horses are the same color

Proof by induction (n=1):
if there is only 1 horse then by definition all horses are all the same color.

Assume it works for case n = k:
As in, any group of k horses are all the same color.

proof for n = k+1:
Take the group of the first k horses, by the assumption those k horses are all the same color. Now take the last k horses... by the assumption all of these horses are the same color. Thus all k+1 horses are the same color.

Since we know it works for k=1, and if case n = k works then case n = k+1 works.

Thus it works for n = 1,2,3,.....

Thus all horses are the same color.



Take that nubs!