On Thu, May 22, 2008 at 3:56 PM, Joachim Faulhaber <afojgo@googlemail.com> wrote:
Incrementability seems also more fundamental to me than Addability. Which is to say that a concept or algebra that offers Addability almost certainly also has a Incrementability, but not the other way round. Take for instance the Peano Axioms of natural numbers, where Incrementability is given in the form of the fundamental successor function.
Not necessarily true. Strings under concatenation (a monoid) are Addable, but incrementing makes little sense. Further, incrementing on even the real numbers doesn't necessarily make sense, at least not when defined in terms of the successor function (which maps integers to integers). Complications also arise in, well, complex numbers. ;) Dates/times are a more unusual case because their underlying representation is integral, but as a physical concept they are continuous (as far as we know). Questions arise especially when considering the granularity of the date/time you are dealing with. Is foo_date+1 24 hours from now, or one second from now? Or perhaps one millisecond... I don't think incrementability is as simple as incrementing the private member of the date_time object. - Jim