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Date: 2002-08-19 05:41 pm (UTC)
From: [identity profile] johnpalmer.livejournal.com
Re: the horses, I thought I'd already proved to you that horses don't exist.

First, you need to understand that all horses are the same color.

You can prove this by induction; one horse is obviously the same color as itself. Then, assume it's true for sets of up to n-1; for a size n set of horses, take one away, and you see that the remaining n-1 horses are all the same color; continue doing this, and you can see that all of the n-1 sized subsets are the same color, so they must *ALL* be the same color.

(nb: Yes, I know... for size 2 sets, this means you take away one horse, and have a single horse that's the same color as itself. It would only work if we proved it for all sets of size 1 and 2, and then assumed it true for up to n-1. It's a joke, okay? :-) )

Then you need to realize that horses have an infinite number of legs.

Proof, by intimidation:

A horse has forelegs in the front, and two legs in the back, for a total of six legs. Six legs is an odd number of legs for a horse to have, but horses have legs in pairs, so they must have an even number of legs.

Well, the only number that is both even, and odd, is infinity. So, all horses have an infinite number of legs.

But... a horse with an infinite number of legs would certainly be a horse of a different color, wouldn't it? And *THAT* doesn't exist by the previous theorem. So, all horses are really imaginary.

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