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From: howardh@ihu1e.UUCP (Howard Hill)
Newsgroups: net.flame
Subject: Wombats
Message-ID: <179@ihu1e.UUCP>
Date: Fri, 13-Jan-84 12:06:50 EST
Article-I.D.: ihu1e.179
Posted: Fri Jan 13 12:06:50 1984
Date-Received: Sat, 14-Jan-84 03:38:42 EST
Organization: AT&T Bell Labs, Naperville, IL
Lines: 42

The argument between Laura and Tim is very amusing because,
you see, wombats do not exist.  I shall demonstrate this by
giving a proof by contradiction.

(1) Assume wombats exist.  If so, they must come in different
colors, e.g. godless red commie wombats, and heathen yellow wombats.

(2) However, I will now show that if wombats exist, they must be
all the same color.  I offer the following proof by induction:

Base step:
    A set consisting of only wombat contains only wombats of one color.

Induction step:
    Given a set of N+1 wombats.  Remove one wombat from this set.
    The resulting singleton set contains only one wombat and obviously
    it contains only wombats of one color.  The resulting set of
    size N (by hypothesis) contains only wombats of one color.
    Therefore the original set of size N+1 contains wombats of
    one color.

Extremal step:
    If wombats were to exist, the set of all wombats would have to
    be a denumerable set.  I have discovered a truly remarkable
    proof for this, however the margin of this screen is to small to
    contain it.

(3) Therefore if wombats were to exist they would both have to be
    all the same color and not all the same color. Since this
    is a contradiction, the hypothesis that wombats exist is false.

I hope this is up to the usual high standards of reasoning and logic
I have seen in net.flame.
-- 

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