Round 6
(ended)
Turn 6 - 31
(ended)
2006-11-19
22:19 CST

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5314

Creator	Jef
Create Date	2006-05-13 22:53
Statement	In reference to Rule 357 "Launch the Alert Vipers!", it is impossible to determine who the Commander(s) are or if there is chaos in the fleet, constituting a paradox as defined by Rule 215.
Arguments	Rule 357 "Launch the Alert Vipers!"(1) specifies, "At the beginning of every turn, the player with highest of target score divided by the sum of style and number of points ((target score)/(points + style)) becomes the Commander." This rule does not indicate that the Commander is chosen only among active players, so inactive players must be included. However, inactive players do not have style values, as Rule 313 "Do it with style"(2) specifies that only active players do. Therefore, it is impossible to complete this calculation for inactive players. Even if the missing argument is considered to be a style value of 0, it is still impossible to determine the status of the Commander, as several inactive players have a point total of 0. This would leave the formula with a denominator of 0. In arithmetic with real numbers, division by zero is considered invalid(3). So, either way the missing style argument is interpreted leads to the inability to determine the status of the Commander, constituting a paradox because it cannot be determined with finality. Rule 215 "The Paradox Rule"(4) thus comes into play and the round should end. REFERENCES: (1) Rule 357 "Launch the Alert Vipers!" (2) Rule 313 "Do it with style" (3) Wikipedia-Division by zero (4) Rule 215 "The Paradox Rule"
Judge	Ouroboros
Decision	True
Reasoning	This paradox is sustained and it is my opinion that it ends Round Six of Nomicron, with Jef declared winner. While the rule in question was too broad in its reference to players both active and inactive, it also did not account for new players with an initial score of zero. As much as we may understand a division by zero to result in no useful numeric value (or no ordinal), it is technically a number that cannot be compared to real numbers. The issue of division by zero could be addressed during the Convention, and defined as a non-number that is removed from comparison.