If zero is an even number, that certainly alters the game of roulette. Both zero, and I imagine double-zero, are now even - meaning I can win exactly fifty percent of the time by betting even.
How does this logic hold up? More importantly, would the pit-bosses in Vegas buy it? 
I confess to some frustration at your rather “uneven” answer, Dex. A bunch of points:
[ul][]In the natural number system, zero is neither odd nor even, because it is no more a part of the system than is -43, pi, or the square root of a negative googol. If the natural numbers are defined as the positive integers, beginning with one and ascending, zero is outside the definition.[]If “even” is defined as an integer multiplied by two, then zero is even, since 2x0=0.[]If even is defined as an alternating sequence with odd, then zero is even, since it comes between -1 and 1, both odd numbers.[]One is not a prime by definition in number theory. But the exclusion is not arbitrary. You use the traditional definition of prime, “a number not evenly divisible except by itself and one.” By this definition, it is. But consider the alternate definition: “a prime is a number with exactly two discrete positive integer factors.” All primes meet this definition; one, having a single discrete positive integer factor, does not.The implications of this alternate definition are intriguing; consider, for example, the category “having exactly three discrete positive integer factors” – it defines some but not all perfect squares, and nothing but. Those it defines are the squares of all the primes.[/ul]
Oh, BTW, the link is http://www.straightdope.com/mailbag/mzeroeven.html
Poly, I don’t disagree., but I don’t understand your frustration. Your first three points are pretty much what I said. I said that zero is even, and I used the definitions you gave. The Poser had some fuzzy idea in the back of her mind that there was some circumstance under which zero might not be even, and I was trying to figure what that might be… hence, the stretch to definitions of even numbers that exclude zero (and all negative numbers.)
I don’t quite get your -43pi example. Odd/even is usually confined to integers, since it’s not a reasonable distinction within (say) the rational numbers – every rational number can be divided by 2 leaving no remainder, so every rational number is “even”. Alternately, every rational number can be written in the form 2X + 1 where X is also a rational number, so every rational number is also “odd”. Hence, the even/odd distinction is ONLY valid for working within a subset of the Reals… such as the integers, the positive integers, the natural numbers, whatever. Thus, it is not unnatural (pun) to say that the definition of zero as even depends on whether it is included in the set under consideration.
On the prime number definition, yeah, sure, again, I don’t disagree nor do I understand your frustration. Repeating, I was trying to find something that would fit the OP’s memory (“neither A nor B”) and thought that might do it. Under most definitions, 1 is neither prime nor composite. Your definition is intriguing, although I’d think that a repeated factor doesn’t count as “discrete”, does it?
Oh, and thanks, Demetrius, good example. I didn’t think of non-mathematical situations where zero might not be classified as even.
Someone else, in the columns forum, I think, commented on the statement
to say that the word “uniquely” is erroneous.
10 = 5 + 5
10 = 7 + 3
.
I have a couple of very minor nitpicks on dex’s generally excellent answer:
Sure it has a remainder, like every division operation. The remainder is zero.
It hasn’t been proven (Archimedes Plutonium nonwithstanding), but as pointed out before, ‘unique’ is not part of the conjecture.
On the “no remainder” vs “zero remainder”, I respond with a shrug of the shoulders.
On the Goldbach conjecture, yes, my apologies, and I will have the word “uniquely” edited out. Thanks for catching it.
It’s easy: +, -, and * have no remainder. / always has a remainder.
Maybe I’m pokey, but if 1 is generally excluded from the list of primes, doesn’t that invalidate Goldbach’s conjecture (i.e., 4 = 3+1 and nothing else)?
Cheers,
Ian
Ian
4 = 2 + 2
6 = 3 + 3
And thanks for the opportunity to flex my math muscles
.
Stay tuned, next week, for Group Theory and the definition of Fields.
CKDextHavn -
Your email doesn’t work, I can’t reply to ya. If you see this, I am fine with what you suggested, Dimitrius is good for the name.
Hmm, dunno why my email doesn’t work…
But in any case, and for those who were wondering, we will amend the Mailbag item to reflect Dimitrius’s comment about roulette… and also to patch the statement of Goldbach’s conjecture.
Thanks for the assists.
I don’t want to be tedious, but it seems to me that the question of how the game roulette treats zero is probably irrelevant to a discussion about mathematically rigorous definitions as they apply to zero.
And why not? I strongly believe that (basic) groups should be part of 4th of 5th grade math curriculum.
Midnight: The original questioner said that she “read something” about zero being neither odd nor even. She did not say she read it in a mathematical treatise. I interpreted the question as a mathematical discussion, but I think that Dimitrius cleverly (and rightly) expanded it to a non-mathematical situation.
Don’t fret being viewed as tedious, tediousness is part of rigorous mathematics, it’s a requirement. But Euclid help us if a Straight Dope Mailbag Answer ever restricts itself to rigorous mathematics!
No repeated factors needed; his definition works fine.
The two discrete factors of 7 are 1 and 7. The two discrete factors of 2 are 1 and 2.
The single factor of 1 is 1.
And the three discrete factors of 49 are 1, 7, and 49.
Should be
if u is a unit:
pp can be written p[sup]2[/sup], (pu) * (p*u[sup]-1[/sup]) …
That is u and v look to me like they are equal
Transitivity of the relation = means:
if a=b and b=c then a=c
From my Mathematics Dictionary (James/James), 4th Edition:
E’VEN, adj. even number. An integer that is divisibly by 2. All even numbers can be written in the form 2n, where n is an integer.
Judges 14:9 - So [Samson] scraped the honey into his hands and went on, eating as he went. When he came to his father and mother, he gave some to them and they ate it; but he did not tell them that he had scraped the honey out of the body of the lion.