From: Factitious (x40_at_pacbell.net)
Date: Wed Feb 06 2002 - 17:01:15 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 0. 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 a proof of that type.
To clarify, all integers must indeed be written out using the 10
hendigits.
>>>>>>
Note:
I don't like reposts much, so I decided to add at least a sentence
of new contribution. The term "hendigit" is by analogy with
"hendecagon". Admittedly this is somewhat different from the process by
which "digit" was coined, but I don't know of a Latin word for a person
with an extra finger. "Polydactyl" might fit that, but it's Greek, so
should not be casually mixed with Latin terminology.
--
Rule Date: 2002-02-07 01:00:09 GMT
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