Posted by Eugene Volokh: Silly supposed math conundrum: I'm amazed how often people think there's some puzzle about whether zero is odd or even. (Do [1]a google search on "is zero even" and you'll see.) The question has even made its way into news stories, usually when some government institutes "odd-even" gasoline rationing in which the days you can buy gas depend on whether the last digit of your license plate is a 0.
The answer couldn't be simpler: Zero is even because it is exactly divisible by 2 (i.e., when divided by 2 it yields no remainder) or, if you prefer, because it is a multiple of 2 (just as 2, 4, and the like are). That's the [2]dictionary definition, and it's also the standard mathematical definition. Nor would there be any reason to define evenness the same way. Mathematical definitions are sometimes chosen with an eye towards convenience, for instance when prime numbers are defined to exclude 1, so as to guarantee that every positive integer above 1 has a unique prime factorization. One could define prime numbers so that 1 is included (any positive integer that's divisible only by 1 and itself) rather than so 1 is excluded (any positive integer that has exactly two different positive integer divisors); but mathematicians have chosen the latter definition for their convenience. Still, I know of no reason why evenness would be defined so 0 wouldn't be even, and I've never seen any such odd definition. (Of course, zero isn't an even positive integer, but that's because it's not positive, not because it's not even. I've also heard it said that in some versions of roulette, if you bet on the evens, you'll lose if the ball lands on 0, but naturally doesn't really tell us much about the mathematical definition.) Incidentally, I once ran across an article whose author was saying some political question was unanswerable, much like the question whether zero is even. I e-mailed him to say that the is-zero-even question is very much answerable. He responded with an apology, and a suggestion that he should have used some other example, such as "Is there an infinite number of primes?" I felt compelled to respond that actually there is an infinite number of primes, and there's an elegantly simple proof developed of this over 2000 years ago (by Euclid). Ah, the perils of drawing analogies to a subject that one doesn't really know well. References 1. http://www.google.com/search?hl=en&ie=UTF-8&q=%22is+zero+even%22&btnG=Google+Search 2. http://dictionary.reference.com/search?q=even _______________________________________________ Volokh mailing list [EMAIL PROTECTED] http://highsorcery.com/cgi-bin/mailman/listinfo/volokh
