gistfile1.txt

/ Lemma: All horses are the same color.   \
| Proof (by induction):                   |
|                                         |
| Case n = 1: In a set with only one      |
| horse, it is obvious that all           |
|                                         |
| horses in that set are the same color.  |
|                                         |
| Case n = k: Suppose you have a set of   |
| k+1 horses. Pull one of these           |
|                                         |
| horses out of the set, so that you have |
| k horses. Suppose that all              |
|                                         |
| of these horses are the same color. Now |
| put back the horse that you             |
|                                         |
| took out, and pull out a different one. |
| Suppose that all of the k               |
|                                         |
| horses now in the set are the same      |
| color. Then the set of k+1 horses       |
|                                         |
| are all the same color. We have k true  |
| => k+1 true; therefore all              |
|                                         |
| horses are the same color. Theorem: All |
| horses have an infinite number of legs. |
| Proof (by intimidation):                |
|                                         |
| Everyone would agree that all horses    |
| have an even number of legs. It         |
|                                         |
| is also well-known that horses have     |
| forelegs in front and two legs in       |
|                                         |
| back. 4 + 2 = 6 legs, which is          |
| certainly an odd number of legs for a   |
|                                         |
| horse to have! Now the only number that |
| is both even and odd is                 |
|                                         |
| infinity; therefore all horses have an  |
| infinite number of legs.                |
|                                         |
| However, suppose that there is a horse  |
| somewhere that does not have an         |
|                                         |
| infinite number of legs. Well, that     |
| would be a horse of a different         |
|                                         |
| color; and by the Lemma, it doesn't     |
\ exist.