From: Factitious (x40_at_pacbell.net)
Date: Tue Feb 05 2002 - 21:38:16 PST

    The statement "fc + rc = (f+r)c unless c is a fantasy number" is false
when f = j, r = 1, and c = 0.  (Note that 0 is a real number and thus not a
fantasy number.)  To show this, I will use my favorite type of proof,
Reductio Ad Absurdum.  In other words, I will show that the statement reduces
to a trivial contradiction, thus demonstrating it to be false.

(j+1)*0 = j*0+1*0           (statement under consideration)
(j+1)*0 = 1+1*0              (definition of j)
(j+1)*0 = 1+0                  (0 times a real number equals 0)
(j+1)*0 = 1                      (0 plus a real number equals that number)
j+1 = 1/0                          (divide both sides by 0)
j+1 = j                              (definition of j)
1 = 0                                (subtract j from both sides)

    1 is, of course, not equal to zero.  This system of math may be
fantastic, but it should not be absurd.
    Since a counterexample exists, "fc + rc = (f+r)c unless c is a fantasy
number" is false.


    I like Reductio Ad Absurdum proofs so much that from now on, all valid
odd-numbered rules must contain at least one.

Rule Date: 2002-02-06 05:37:10 GMT

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