Thanks - I'll probably take you up on that sometime. ;)

I fully realize that I'm stubbornly refusing to accept something regarded as rigorously proven canon by a very large number of people who are both smarter and better trained in arcane mathematics than I am.

Y'know, having written this proof, I'm not so sure the proofs are that rigorous. It's sorta definitional, in some ways. (Then again, all math is. :D )