In MS Excel, the iseven function truncates the argument, so 2.5 is even in that world. VB gives our C example, above.

Google gives about 48000 hits for the term “iseven”, a likely name for the function.

The best legal answer I can see is Coe’s answer, because code is law (see Larry Lessig.)

Unfortunately that doesn’t explain how you decide it’s an odd number. Maybe the logical process is, “everything must be even or odd” (actually, a false premise if “everything” includes reals, etc.), “0 is not even”, hence “0 must be odd”.

It IS a number in the sense that it is a placeholder.

It’s position in connection with numbers that are also divisible by “2″ should have made this painfully obvious.

Ig not, count backwards, starting at ten if you like, and then you’ll arrive at the number before “1″, which is the smallest odd number.

The confustion comes in here for ZERO’s place in the notion of “null” or “nothingness.”

Take it up with the mathematicians and before them, the mysticism of the Hindus who created this notion of “something that is, yet is not” simultaneously.

It is one of those nifty elements the Western world uses on a daily basis in ratio-centric thinking and smug snarkyness about its superior reasoning skills to the mystic muck of the old world, but nontheless is used fairly much as is.

“That which is, and yet is not”

Half-dead kitty-cats have met their match here.

singed,

(a real estate appraiser in South Carolina)

math person:
Actually, he is right, but both of you seem confused about what a whole number is. It means “not a fraction”, and is exactly the same as integer, be it positive, negative, or 0. What you are thinking of is natural numbers, which is positive integers, and possibly 0, depending essentially on personal choice.So yes, 0 is whole, and so it’s even, but whether one chooses to call it natural or not is irrelevant.

Strictly speaking “not a fraction” is NOT the same as “integer”. For example, PI (or any irrational number) is “not a fraction”, but is also not an integer.

what then for 0?

Proof: We will prove this by induction. 1 is interesting since it is the multiplicative identity and is neither prime nor non-prime. 2 is interesting because it is the only even prime. 3 is interesting because it is the smallest odd prime. Assume that a positive integer k is the last interesting positive integer. That means that the integer k+1 is the first uninteresting integer. Isn’t that interesting?

Off Kilter: As I write this, over 50% of voters think it is possible for something to be either BOTH odd AND even, or NEITHER odd NOR even. Wow.Eagerly awaiting EV’s quiz on 4 sided triangles…

Pi is neither odd nor even. So, yes its perfectly possible for something to be neither.

Infinity may be both odd and even. Think of a switch. You will be switching it on and off for one second. The first switch will occur at 1/2 a second. The next at 3/4, then 7/8, then 15/16, and so on… When exactly one second has expired, is the switch on or off? Both? Neither?

Sorry bout that.

Better question is whether 0 != -0.

Back before sanity took hold and mod 2 arithmetic slew all others, some computers used the more ‘intuitive’ sign-magnitude arithmetic .. which had the property of allowing 2 different numbers for 0 (“+0″ and “-0″). One beast I worked on would “jump on zero” for both “+0″ and “-0″. But if you did the “skip if unequal” instruction, it would skip when comparing “+1″ and “-1″. What was worse is that which “zero” you got depended on how you got there (adding to a negative number, or subtracting from a positive number).

Needless to say, those days have since passed and computers nowadays use the 2′s complement arithmetic, which has less quirkiness (the main one being that the negative of the largest negative number is itself).

Cheers,

kdackson: Yankee: I’d wager they think that because it’s divisible by 1, it’s odd.

Eh? 2 is divisible by 1, do you think it is odd?

The issue is, in our numbering system we use it as an even number in counting up or down…+2, +1, 0, -1, -2…

I wonder how many of the commenters arguing this point would ridicule someone who sees the world wholly in subjective terms.

When most people first heard of odd and even numbers, some of them probably learned that numbers that end with 1, 3, 5, 7, or 9 are odd, and numbers that end with 2, 4, 6, 8, or 0 are even. The advantage of this rule is that if one can memorize this rule, one can figure out whether any number is odd or even just by looking at it, and one need not know anything about multiplication or division to do that determination. And if you do know a definition of odd and even numbers based on multiplication or division, you will find that the rule is still true.

In fact, the only significant objection that mathematicians would have to the original rule is that they would say that the rule applies to integers as opposed to all numbers.

Bruce Boyden: Mathematics cannot give you the answer as to ordinary usage. You have no bottles of milk. Do you have an even number of bottles?

Actually, it can. If you add one more bottle, your number becomes odd. So, yes, you do have an even number of bottles.

In fact, by combining zero and even in the same question, one essentially removes the ambiguity of “ordinary usage”. Under ordinary usage we can talk about a surface being “even”, but that clearly does not apply here. We can talk about an “even” amount, which basically means “just right”–again, that makes little sense here. We can talk about dividing something evenly, but the context does not specify division. If we are going to introduce division into the context, however, there is no reason not to rely on a minor mathematization of the question–can 0 bottles be divided evenly between two people? And, of course, the answer is “Yes”–both get the same number of bottles, none!

So, you can stretch it any way you like, but the fact remains that 0 is an even number.

2 is an odd number.

Proof: 2 is the only even number that is prime. Isn’t that odd?

However, there are worlds beyond the simple definition where zero’s status is a bit fuzzier, like with goldbach’s conjecture. Are they trivial or unusual enough to disregard? Perhaps, but they’re still there. There used to be some debate about whether one was prime, as it violates one of the uniqueness part of a prime’s identity. A little ambiguities not a bad thing here. It allows for a greater appreciation of the subject.

Off Kilter: As I write this, over 50% of voters think it is possible for something to be either BOTH odd AND even, or NEITHER odd NOR even. Wow.

Eagerly awaiting EV’s quiz on 4 sided triangles…

I wouldn’t hold your breath. On the other hand, spherical triangles are pretty interesting. I did, however, fail at teaching myself how to solve spherical trig problems though outside of triangles with at least two right angles (which are easy).

Sara: Hey!McGraw-Hill’s Catholic High School Entrance Exams, 2ed:Zero is an interger that is neither even nor odd.

Sara… but that is for Catholic School entrance exam… ;) (I’m a recovering Catholic.)

Deezrightwingnutz: If I recall, any number divided by zero is “undefined,” except 0/0, which is “indeterminate.” I don’t know what the hell the difference is, so I’m not going to make fun of someone who forgot what he memorized for a test back in 11th grade.

Re “undefined” vs “indetermine” the answer becomes apparent when starting to do basic calculus and it has to do with questions of limits.

Suppose I take the limit of 1/x as x goes to 0. As x goes to 0, 1/x goes to +/- infinity. Same with 1/2x and 2/x. This isn’t strictly defined because the limit approaches different values from different sides of the graph (from the negative side, it approaches negative infinity, and from the positive side infinity or possibly vice-versa depending on the equation).

Now, consider the following equations: 3x/4x^2, x^2/4x, and 8x/x and take the limits there as x goes to 0. In the first case, the limit if 3x/4x^2 goes to +/- infinity, x^2/4x goes to 0, and 8x/x goes to 8. Hence while the limit of any number divided by 0 can be defined as approaching infinity or negative infinity in any case, many equations which could yield 0/0 could result in ANY limit. These could result in a defined limit, but of the infinite number of equations that could create a limit, any possible answer is possible.

Hope this helps, but it has been 15 years since I took a math class.

What’s your angle, Off Kilter? Anyway, I find your response obtuse (demonstrated a lack of acuity). And a response has to be either obtuse or acute, right?

Not quite. The angle would either have to be acute or obtuse if it is not right (or correct). Therefore “acute” and “obtuse” display the different quantities of wrong (not “right”) points of view (i.e. “angles of approach”).

steve: forget the math nerd rationale.zero is nothing.numbers that are odd and numbers that are even are something… and something can’t be nothing…. so zero is neither odd nor even.

Finding less than 50% of VCers failing to identify 0 as an even number is troubling enough. But someone actually dragging out this dinosaur of an argument combined with an anti-intellectual snark is just plain offensive.

There is no debate possible here–a definition is simple and precise. Any measure by which you may approach the definition, 0 will end up being even. Not both, not neither–only even.

It is important to note that Aristotle did not have a concept of 0 at all. For that matter, Aristotle did not think that 1 was a number either–1 was a unity, a whole and thus could not be counted. So, if Volokh readers were contemporaries of Aristotle, they would get a pass. But they are not, therefore, they are illiterate.

Thanks for the laugh, Eugene. Next, ask how many of your readers believe that the Earth is flat.

What is the remainder of 0/2? Feel free to use a calculator.

I like to think that Eugene is simply trying to expand lawyer’s knowledge of math beyond calculating billable hours.

Given the poll results, this is an extremely useful public service.

I mean, really, this is basic, basic stuff. And fine, not remembering a (simple) definition from school outside your core professional pursuit isn’t anything anyone will hold against you. But fighting about simple definitions in math that would mean the world would be a very different place if they were incorrect, even as a lawyer, isn’t something I’d bet the vacation home or the nanny on.

The integer 0 is even and is not odd.

There is no rational reason to exclude zero from the definition of even numbers since it meets ALL of the tests.