Isn't "natural" supposed to connote a strictly positive integer?
In Germany and algebra, yes. In France and number theory, zero is natural.
This discussion reminds me of a very funny post to sci.math back in 1993 by Jan Willem Nienhuys in reponse to one of the discussions about whether or not 0 is a natural number: Here's a copy of his message: ----begin copy------------------ From: Jan Willem Nienhuys (wsadjw@rw7.urc.tue.nl) Subject: Natural numbers start with 2. Newsgroups: sci.math Date: 1993-04-14 06:44:33 PST The natural numbers start with 2 (TWO). The name "counting numbers" make that clear. If there's only one item of a certain kind, one doesn't start counting. Moreover, for most mathematicians, counting stops at two as well, as anything larger than 1 is denoted by `n', which is synonymous with `many, I don't care how many'. Consequently, 3 must be supposed to be infinity. The symbol for infinity is two 3's on top of each other. This explains the mystery of Trinity. I hope this simple solution will stop the silly discussions about 0 being a natural number. My hope will be in vain, I know. JWN ------------end copy------------------------------