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.
QED.
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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