# Is Zero odd or even

July 3, 2004 9:37 PM Subscribe

The Number Zero: odd, even, or neither?

Response by poster: Thanks Bob. I heard from my second grade teacher (years ago) that zero was neither even nor odd. I'd reasoned it out about as far as that article, but I too came up at a loss for a reason to call 0 anything but even.

posted by Phatty Lumpkin at 9:54 PM on July 3, 2004

posted by Phatty Lumpkin at 9:54 PM on July 3, 2004

Neither. Remember your Cartesian co-ordinates and integers. 0 is smack dab between -1 and 1 for a reason.

It has no value, therefore it cannot be divided, so therefore it cannot be odd or even, because you must divide a number to determine if it is odd or even.

IANAM, though. That just makes sense to me, logically.

Though, it does make a sort of sense to look at the sequence of -2, -1, 0, 1, 2 and assume 0 is even because -1 and 1 are odd and -2 and 2 are even.

posted by loquacious at 2:59 AM on July 4, 2004

It has no value, therefore it cannot be divided, so therefore it cannot be odd or even, because you must divide a number to determine if it is odd or even.

IANAM, though. That just makes sense to me, logically.

Though, it does make a sort of sense to look at the sequence of -2, -1, 0, 1, 2 and assume 0 is even because -1 and 1 are odd and -2 and 2 are even.

posted by loquacious at 2:59 AM on July 4, 2004

Hrm, reading the Straight Dope article, and zero does meet the division requirement for odd or even.

Still thinking logically and intuitively, and not as a mathematician, I'll protest - even in ignorance - and say it is neither odd nor even. It has no value to divide into two equal parts.

posted by loquacious at 3:04 AM on July 4, 2004

Still thinking logically and intuitively, and not as a mathematician, I'll protest - even in ignorance - and say it is neither odd nor even. It has no value to divide into two equal parts.

posted by loquacious at 3:04 AM on July 4, 2004

Even.

I hate that there really is subtle interesting mathematics to think about, and people get tripped up by this one.

Even the question about whether 1 is prime or not is more interesting. In that case, 1 fits all the criteria to be prime -- its only divisors are 1 and itself, for example. But we explicitly rule it out, so that we can reap the benefits of unique factorization, which is what primes are for in the first place. If we allowed 1 to be prime, then unique factorization would go out the window.

posted by gleuschk at 6:57 AM on July 4, 2004

I hate that there really is subtle interesting mathematics to think about, and people get tripped up by this one.

Even the question about whether 1 is prime or not is more interesting. In that case, 1 fits all the criteria to be prime -- its only divisors are 1 and itself, for example. But we explicitly rule it out, so that we can reap the benefits of unique factorization, which is what primes are for in the first place. If we allowed 1 to be prime, then unique factorization would go out the window.

posted by gleuschk at 6:57 AM on July 4, 2004

Even. It fits the definition perfectly (except, as the Straight Dope points out, at the roulette table).

You know, if I saw a question asking whether quantum theory was compatible with general relativity, I probably wouldn't jump in to say "I know jack shit about physics, but it seems to me they have to be compatible, because hey, it's the same universe, right?" When answering an AskMe question (or, indeed, any other) it helps to actually know something about the subject. But that's just me.

posted by languagehat at 7:52 AM on July 4, 2004

You know, if I saw a question asking whether quantum theory was compatible with general relativity, I probably wouldn't jump in to say "I know jack shit about physics, but it seems to me they have to be compatible, because hey, it's the same universe, right?" When answering an AskMe question (or, indeed, any other) it helps to actually know something about the subject. But that's just me.

posted by languagehat at 7:52 AM on July 4, 2004

The University of Baltimore has a historical perspective on zero's origins.

posted by Smart Dalek at 7:59 AM on July 4, 2004

posted by Smart Dalek at 7:59 AM on July 4, 2004

Not so much the U. of Baltimore as just some professor. A well-regarded one, it appears, but still just one guy. This history from the MacTutor History of Mathematics site (which is a fantastic resource) is perhaps a little more authoritative.

Also, because it's still bugging me, I need to rail just a little bit about the "zero is a concept, not a number" or "has no value" idea that appears above. Numbers

posted by gleuschk at 8:24 AM on July 4, 2004

Also, because it's still bugging me, I need to rail just a little bit about the "zero is a concept, not a number" or "has no value" idea that appears above. Numbers

**are**concepts. The value of a number is**precisely**the number itself. There isn't a differentiation here; there's just a failure of (imprecise, everyday) language to describe something that is abstract, but has a very precise meaning.posted by gleuschk at 8:24 AM on July 4, 2004

*You know, if I saw a question asking whether quantum theory was compatible with general relativity, I probably wouldn't jump in to say "I know jack shit about physics, but it seems to me they have to be compatible, because hey, it's the same universe, right?"*

That's a little snippy there, languagehat. The first major difference between zero and quantum theory is that

*everyone*has a daily relationship with zero. Even unlearned schmoes are entitled to an opinion that's intended to be helpful in response to a question that had no prereqs. Leave it to the threat originator to declare participants unhelpful.

posted by squirrel at 10:52 AM on July 4, 2004

More Mathematically:

However, if you get in to serious math, you find that the numbers are just symbols. Their meaning depends entirely upon the model you happen to be working within.

More on zero.

posted by Kwantsar at 12:42 PM on July 4, 2004

*In mathematics, any integer (whole number) is either even or odd. If it is a multiple of two, it is an even number; otherwise, it is an odd number. Examples of even numbers are -4, 8, 0, and 70. Examples of odd numbers are -5, 1, and 71. The number zero is even, because it is equal to two multiplied by zero.*However, if you get in to serious math, you find that the numbers are just symbols. Their meaning depends entirely upon the model you happen to be working within.

More on zero.

posted by Kwantsar at 12:42 PM on July 4, 2004

...besides, in QM, as everyone already knows, even and odd is meaningless---selection rules are all that matters.

posted by bonehead at 12:43 PM on July 4, 2004

posted by bonehead at 12:43 PM on July 4, 2004

*The first major difference between zero and quantum theory is that*

*everyone*has a daily relationship with zero. Even unlearned schmoes are entitled to an opinion that's intended to be helpful in response to a question that had no prereqs.I disagree. "Everyone" has exactly the same relationship with zero that they do with quantum theory, namely that they live in a world that requires both for scientific description. But you no more encounter "zero" in your daily life than you do quantums; both are scientific/mathematical concepts that took many centuries to be developed and are widely misunderstood by laymen. One reason I get snippy is that people are constantly providing false "answers" to questions about language on the basis that they speak one and therefore know all about it; this is just as silly (as I frequently repeat) as thinking you can answer questions about the spleen because you have and use one. But by all means respond to any question that appeals to you. Your freedom of speech allows you to do so, just as mine allows me to point out the fact that the response wasn't helpful.

posted by languagehat at 10:03 AM on July 5, 2004

Response by poster: Doubtful if anyone is still checking this, but I'm still thinking about it. In a sense, one way to prove zero to be neither odd nor even would be to prove that it's both. Zero meets the criteria for evenness by being divisible by two, without remainder. Are there any tests for oddness, or sets of all odd numbers which have a pattern and could include zero? If so,

Thoughts?

posted by Phatty Lumpkin at 12:45 AM on July 7, 2004

*that*might be grounds for claiming zero is neither even nor odd.Thoughts?

posted by Phatty Lumpkin at 12:45 AM on July 7, 2004

I think that by still posting to this thread we've both passed the test for oddness, Phatty. ;^)

posted by squirrel at 11:24 AM on July 7, 2004

posted by squirrel at 11:24 AM on July 7, 2004

A reasonable thought, Phatty, but "odd" is defined to mean "not even". You could try to finesse this by saying that

Even if there were some other way to define oddness, it would either be consistent with the definition above (in which case we're back where we started) or inconsistent (in which case either the whole house of cards tumbles down on our heads, or you've defined "odd" to mean "red" or something equally unuseful).

posted by gleuschk at 9:48 AM on July 20, 2004

*n*is odd if division by 2 leaves a remainder of 1, but that's just a longwinded way of saying the same thing.Even if there were some other way to define oddness, it would either be consistent with the definition above (in which case we're back where we started) or inconsistent (in which case either the whole house of cards tumbles down on our heads, or you've defined "odd" to mean "red" or something equally unuseful).

posted by gleuschk at 9:48 AM on July 20, 2004

This thread is closed to new comments.

posted by ascullion at 9:41 PM on July 3, 2004