Legal Commentary

Yow!

By Eugene Volokh

I was shocked at the number of people who took the view that 0 was neither even nor odd. (I was even more shocked by those who thought 0 was odd, and by those who thought 0 was both even and odd, but there were comparatively few of those.) Under every definition of even that I’ve ever seen, and under every one that to my knowledge has any mathematical utility, an integer is even if it is divisible by 2 with no remainder. 0 is divisible by 2 with no remainder (0/2=0). Therefore, 0 is even. End of story, though if you want much more of the story, read this monster comments thread.

But what shocked me even more was a link to McGraw-Hill’s Catholic High School Entrance Exams p. 213 (2d ed. 2009), which asserts (twice) that “The number zero (0) is an integer but is neither even nor odd.” As I said, this departs from all that I’ve ever seen of actual mathematical definitions. And the material in the book is actually inconsistent with that very definition; for instance, later in the page, it says that

(even integer) +/- (even integer) = even integer
…
(odd integer) +/- (odd integer) = even integer

But that of course is wrong if 0 isn’t even, and right only if 0 is even. (Consider 2-2 and 3-3.) And of course these equations, and many others, are part of the reason that having 0 be even is such a useful definition, one that mathematicians have settled on.

In any case, this assertion in the book can’t be doing its readers any good. I tried to find an e-mail address to which I could complain, but I couldn’t. If any of you can let me know whom I can contact on this, I’d much appreciate it.

Full post as published by The Volokh Conspiracy on September 30, 2009 (boomark / email).