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Comment by patio11 | Hacker News Reader

Well, because it's defined to be even.

This implies that defining it to be odd would be an acceptable choice. Defining zero as odd would break almost every generalization you can make about even and odd numbers.

And even number plus an even number is even. An even number plus an odd number is odd. And odd number plus an odd number is even.

Oh, whoops, zero was odd? Sorry, let me rephrase: "And even number plus an even number is even. An even number plus an odd number is odd. And odd number plus an odd number is even. SPECIAL CASE: IGNORE ALL THAT IF ONE OF THE NUMBERS IS ZERO."

Numbers alternate odd, even, odd, even, odd, even. EXCEPT AROUND ZERO.

Even numbers can be written as 2 * k, for k is some integer. Odd numbers can be written as 2 * k + 1, for k is some integer. EXCEPT FOR ZERO.

Even numbers can be divided into two equal parts by two. Odd numbers can not. EXCEPT FOR ZERO.

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Arguing along those lines has some interesting results. How can -2 be a number? If you have two apples, and I have none, you can give me two apples. <b>You can't give me -2 apples.</b>

You want zero diamonds? I can SHOW you zero diamonds. You can take zero diamonds from me anytime you want. I'll just make more!

There's something special about 0. And it's right next to 1, which is the mother of all other integers. And zero looks way more pregnant than 1.

Zero is more like the absence of a number (which is why it was invented to be a placeholder). In physics there are electron holes, etc., they're called quasi-particles. There are no magnetic monopoles (yet) but there are quasi magnetic monopoles ... that carry current.

So maybe the day will come when zero becomes a quasi-number. Or better still, a DWARF number. And some people's mathematical kids will write threatening letters to the New York Times.

Which is why it was defined as even. Similar reasons apply for why one is not considered a prime number.

Not really. The set of even integers is 2Z = {2k | k is an integer}. 0 is in that set.

The set of odd integers is 2Z+1 = {2k+1 | k is an integer}. 0 is not in that set.

The reason we don't like 1 being prime is because it makes stating lots of theorems that involve primes (in particular, the fundamental theorem of arithmetic) really tedious. Instead of saying "For every prime p" or "Let p be a prime" you'd have to say "For every non-unitary prime," etc.

Zero being even is a consequence of the above definition of even, while one not being prime is a choice for our sanity.

The reason we don't like 1 being prime is because it makes stating lots of theorems that involve primes (in particular, the fundamental theorem of arithmetic) really tedious.

No, it makes the FTA wrong! If one were prime, then every number would have infinitely many prime factorizations instead of one unique one.

you'd have to say "For every non-unitary prime," etc.

In the even/odd case, one could just as easily say "for every non-zero odd number." This isn't somehow an argument that applies only to the question of one's primality.

Zero being even is a consequence of the above definition of even

...as is one not being prime a consequence of the definition of primes. A prime is a number with exactly two distinct factors. One only has one distinct factor, therefore it is not prime.

If you don't buy this definition, or if you claim that I'm gerrymandering the definition to suit my preference that one not be prime, be aware that a reasonable person could make the same claim about the definition of even numbers, viz., that it was chosen for convenience. While it's might be entertaining to argue about such chicken-and-egg problems, at the end of the day the evidence is pretty clearly in favor of the properties proceeding from the definition in both cases.

Hmm, I wouldn't say that defining a prime number as a number n with prime factors 1 and a with 1 and a not necessarily distinct instantly breaks the FTA, but it sure does make it a lot harder to state while still conveying the same idea otherwise.

Gotta pick what you're defining and what you're deriving.

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