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devil duck

A mathematical-social puzzle

Last week Governor Chris Christie imposed even/odd-day gas rationing in much of New Jersey, elaborating that "for purposes of this rule, 0 is treated as an even number." Today Mayor Bloomberg imposed even/odd-day gas rationing in New York City, saying among other things
Vehicles with license plates ending in an even number or the number “0” can make purchases of motor fuel on even numbered days.


Why is it necessary to single out 0 and "treat" it as an even number? Is there some planet on which 0 is not an even number? Is there some doubt in somebody's mind, somewhere, that 0 is an even number? Is the evenness of zero somehow culture-specific?

Comments

Because some idiot, somewhere, is going to try to argue that 0 is neither even nor odd and he can get his gas on either day (and probably be insufferably smug while doing it). Adding a sentance prevents that argument from even happening, and doesn't lead the cops or the gas station attendants from having to get into a mathmatical argument when they have other things to do.

That's the real question. Why would some idiot try to argue that 0 is neither even nor odd, as opposed to some idiot trying to argue that, say, 1 or 2 is neither even nor odd?
Because they don't really understand it, their school didn't explain it well, or they are counting on the person doing access control not understanding it.

Also, I will say that I have three post-secondary degrees. I cannot explain to you if 0 is even or odd. I would look at the scheme and go "well, 0 goes on the even days, THAT MAKES SENSE" but the "why" is not something I udnerstand.
OK, here's why 0 is even. In fact, two different explanations.

The even numbers are defined as the numbers which are 2 times an integer. 0 is an integer, so 2 times 0 is an even number.

Alternatively... the integers are partitioned into even numbers and odd numbers in alternation. If you start with an even number, the integers before and after it are odd; if you start with an odd number, the integers before and after it are even. 2 is even (I hope there's no dispute about that!), so 1 is odd, so 0 is even.
Because most people are a) mathematical idiots and b) malicious, greedy, and willing to shiv their own mother to get ahead.
What are the instructions for vanity plates with letters?
According to the Mayor's office,"Vehicles with licenses plates ending in a letter or other character can make purchases on odd numbered days."
Bleh, that sort of breaks the even division of numbers doesn't it! I'd have suggested breaking up the letters...but then again I'm not a politician.
Not necessarily a bad thing, since there are more odd-numbered days than even-numbered days. (7 more per year, or 8 more in a leap year.)
true. but swelpmegod i hope rationing never goes on THAT long.
I think it's more a question of (to the non-mathematical) if zero is even a number!
That's a more legitimate question, and one that bothered philosophers for hundreds of years. For that matter, some seriously questioned whether 1 was a number (on grounds that "number" implies plurality).

But once you've accepted that 0 is a number, there's no conceivable justification for saying it's not even.
On a slightly different topic, why is 1 treated as special when discussing primality? A prime number is defined as having no integer factors other than itself and 1; 1 has no integer factors other than itself and 1, therefore, 1 is prime.

primes

That always puzzled me too until I took a course in ring theory. The definition of "prime number" is a special case of the definition of "prime elements in a ring" (the integers being a very well-known example of a ring).

A unit is any element of a ring that has a reciprocal: in the integers, the only units are 1 and -1. An element p is prime if, whenever p divides rs, either p divides r or p divides s. But since units divide everything, it's sort of a cheap shot to count them as prime.

By contrast, an element p is irreducible if p cannot be written as the product of two non-units. In other words, if p = rs, then either r or s is a unit. Again, units satisfy this as a sort of "cheap shot" -- if p = rs is a unit, then both r and s are units -- and units are normally excluded from counting as irreducible. In the integers, primes and irreducibles are the same; in some other rings, they're not.

What about 0? It's clearly not irreducible, since it can always be written as a product of two non-units -- 0 and any non-unit you care to choose. OTOH, 0 would be prime, since the "whenever 0 divides rs" part never happens unless rs is itself 0, which (at least in an integral domain) implies that either r or s is zero. Except that the definitions of both "irreducible" and "prime" explicitly exclude both 0 and units.

Edited at 2012-11-09 11:49 pm (UTC)
I think the answer to the question is more social than math. If someone sees potential gain for themselves, they will argue all kinds of preposterous things. Arguing over the classification of zero is nothing for such a person (see what I did there?)