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From: anderson@uwvax.ARPA (David P. Anderson)
Newsgroups: net.jokes
Subject: All horses are black: inductive proof
Message-ID: <433@uwvax.ARPA>
Date: Fri, 28-Sep-84 02:33:24 EDT
Article-I.D.: uwvax.433
Posted: Fri Sep 28 02:33:24 1984
Date-Received: Wed, 26-Sep-84 04:16:05 EDT
Organization: U of Wisconsin CS Dept
Lines: 20

<>
In response to a recent request:

Lemma: all horses are the same color.

Proof:  We will show by induction on n that in any set of n horses,
no 2 are colored differently.  This is clearly true for the empty set.
Now assume it's true for n-1, and let X be a set of n horses.  Let y be
an element of X, and let Y be X with y removed.  By induction all the
horses in Y are of the same color.  Similarly, choose z in X, z != y,
and let Z be X with z removed.  Again, Z is all of the same color.
Let h be in the intersection of Y and Z;  y and z are both the
same color as h, so all the horses in X are the same color.

Theorem: all horses are black.

Proof:  Clearly there exists a black horse.  Now apply the Lemma.

Now that that's settled: does anyone remember the proof that
all functions are continuous?