Holy circular reasoning, Batman! The premise of your theorem, that there is such a total order, is equivalent to the existence of such a numbering function. Y

Holy circular reasoning, Batman! The premise of your theorem, that there is such a total order, is equivalent to the existence of such a numbering function. You're saying "A must be true because B is true", where B is just an identical version of A, disingenuously obfuscated by a thin veneer of mathematics! http://en.wikipedia.org/wiki/Fashionable_Nonsense http://en.wikipedia.org/wiki/Fashionable_Nonsense This all ignoring the fact any such "total order" is going to be highly variable through time (today's top engineer is tomorrow's dementia patient is yesterday's toddler)!