From: Stephen Turner (sret1_at_ntlworld.com)
Date: Wed Feb 06 2002 - 01:45:02 PST
Anyone who hasn't yet submitted a rule now has less than 6 hours to do so.
In addition, Alan's and Jonathan's eligibilities both expire shortly after
that, and Factitious has less than a day left.
It's been great to have so many players in this round, and I hope that you
will all want to continue into the second week!
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176:8 INVALID +2.0
Factitious Wed 2002-02-06 05:37:10
>>>>>
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.
<<<<<
Judgement: I interpret "all numbers in base 11" in 176:1 to imply that all
numbers must be written in digits. But this rule contains the words "zero"
and "one". (cf "must each contain at least 1 fantasy number" in your first
rule).
Style: I like the proof, and the restriction. Also, the rule ties up a few
loose ends. It was only invalid on a technicality, so I still give it +2.
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ROUND 176 Round start: Wed 2002-01-30 15:32:50
Player Style Valid until
------ ----- -----------
Ed Murphy - 0.5 Mon 2002-02-11 22:23:30
Rich Holmes + 2.0 Fri 2002-02-08 02:42:41
Factitious + 4.0 Thu 2002-02-07 00:23:06
Jonathan Van Matre - 2.5 Wed 2002-02-06 18:03:06
Alan Riddell + 2.0 Wed 2002-02-06 16:50:44
Others 0 Wed 2002-02-06 15:32:50
James Willson - 2.0 (Tue 2002-02-05 15:32:50)
All times are in GMT and base ten.
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Rule By whom When Judgement Style
---- ------- ---- --------- -----
176:1 Alan Riddell Wed 2002-01-30 16:50:44 VALID + 2.0
176:2 Jonathan Van Matre Wed 2002-01-30 18:03:06 VALID - 2.5
176:3 Ed Murphy Wed 2002-01-30 19:44:52 VALID - 1.5
176:4 Factitious Fri 2002-02-01 00:23:06 VALID + 2.0
176:5 Rich Holmes Fri 2002-02-01 02:42:41 VALID + 2.0
176:6 Ed Murphy Mon 2002-02-04 22:23:30 VALID + 1.0
177:7 James Willson Tue 2002-02-05 08:51:33 INVALID - 2.0
177:8 Factitious Wed 2002-02-06 05:37:10 INVALID + 2.0
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--
Stephen Turner, Cambridge, UK http://homepage.ntlworld.com/adelie/stephen/
"This is Henman's 8th Wimbledon, and he's only lost 7 matches." BBC, 2/Jul/01
--
Rule Date: 2002-02-06 09:57:59 GMT
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