More messages I didn't realize weren't being sent to the group....[mark] On Wed, Feb 8, 2012 at 7:13 PM, Stephen J. Turnbull firstname.lastname@example.org:
Mark Janssen writes:
The math (in my world) simply decided that factorial(0)=1 as the convention of "an empty product" (Wikipedia::Factorial).
In modern math (ie, post-Eilenberg-Mac Lane), it's not really a convention (unlike, say, Euclid's Parallel Postulate); it's the only way to go if you want the idea of product to generalize. If you don't understand that, I have serious doubts that you know what you're talking about. If you do understand that, please take care to be more precise.
Awesome. I didn't know anyone else really understood this kind of issue.
Yes, I want the idea to generalize. In this case, not of "product" and arithmetic (in a mathematical space), but of "object model" and the notion of "grouping" (in a set-theoretical space). So a formalization must be made, and perhaps this arena will be the place to do that.
I have to say that I'm approaching this from in the domain of computer science, so in some ways creating a definition in a new "space", or at least a space separate from the Platonian "Abstract" of mathematics.
Love it! cheers!