On Mon, 25 Jul 2016, nichdel wrote: > On 07/25/2016 12:42 PM, Kerim Aydin wrote: > > Are numerical Switches inherently ordered? > > Probably not, but that doesn't necessarily break anything. > > Number theory tends to define with sets (which are unordered on their > own), but the first-order functions (namely successor) are also defined > on important sets. Integer is an extension of the natural numbers set, > and extends its definitions for first-order functions. It looks like the > rules that define numeric switches reference well-defined sets. > > We may have a problem if a rule defines a value as something that is not > a number-theory set though. For instance, I don't think there'd be an > ordering to a switch defined as being "valid numbers" or "valid decimal > numbers".
This is more for new hypothetical rules; I'm re-writing Cards to go with the new economy, and this includes concepts like "decrease cards by N" or "divide cards by 2". Cards-as-punishment shouldn't be tradeable and are aspects of a Person's status, so "switch" is more amenable than "currency" (besides, we don't have currencies defined yet). I'm trying to see what's the minimal amount of definition I'll need to provide (e.g. "decreases below 0 are set to 0; dividing always rounds down").
