Horses have an even number of legs. Behind they have two legs, and in

front they have fore-legs. This makes six legs, which is certainly an

odd number of legs for a horse. But the only number that is both even

and odd is infinity. Therefore, horses have an infinite number of

legs. Now to show this for the general case, suppose that somewhere,

there is a horse that has a finite number of legs. But that is a horse

of another color, and by the [above] lemma ["All horses are the same

color"], that does not exist.

- Every Horse has an Infinite Number of Legs (proof by intimidation)

Horses have an even number of legs. Behind they have two legs, and in front they have fore-legs.... - 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.... - Theorem: Every horse has an infinite number of legs
Horses have an even number of legs.

Behind they have two legs, and in front they have fore legs.... - Proof techniques #2: Proof by Oddity.
SAMPLE: To prove that horses have an infinite number of legs.

[1] Horses have an even number of legs. [2] They have two legs in back and fore legs in front.... - Proof techniques #2: Proof by Oddity.
SAMPLE

To prove that horses have an infinite number of legs.... - 1] Alexander the Great was a great general.
[2] Great generals are forewarned.

[3] Forewarned is forearmed. [4] Four is an even number.... - 1) Alexander the Great was a great general.
(2) Great generals are forewarned.

(3) Forewarned is forearmed. (4) Four is an even number....