On Thu, 6 Dec 2007, Geoffrey Spear wrote: > Indeed, if hours of research could only find 1 example of this type of > usage of a term and even that usage wouldn't apply in this case I'd > say it's been pretty well established that in a mathematical context > the term decrease isn't used to mean anything but to make a value less > than it is.
Just a point of clarification. Actually, there were many, many, examples, I just meant that 99% of the examples fell into this one class of usage. The problem is one of abstraction. All of the usages, as you say, were "making something less than it is." But a side-result is that it makes some property of the system "more" than it is. For example, making less negative ions than there were happens to increase a secondary parameter "charge" which is the sum of the ions. In this case (this was the difficulty I kept going back and forth on) there was nothing abstracting the items removed from the net property (which one could argue means you couldn't decrease a positive amount, either). Therefore, we're forced to ask if a "parameter" can be reasonably interpreted as an arbitrary set of things with net properties summing to VVLOP, since there's an operation in the rules (the mechanism in question) which specifically allows such changes to be made if we do make this interpretation. Since the rules don't define a parameter clearly (whereas they would define something like a "number"), we can reasonably abstract it into a mathematical concept (sets) which allow the operation, and if can be so abstracted. If an abstraction can be made which specifically supports a mechanism defined in the rules, it should be allowed. This last statement is where "reasonable" comes in-- it is my working principle when presented with two reasonable directions, to err on the side of that which specifically enables rather than disables rules-defined mechanisms. YMMV on this last point, which is why we give judges turns to push in their own directions, and respect the pushing from both sides as long as it doesn't enter the realm of the ridiculous. -G.
