# is 0 even or odd?

#### 2012 Wont Happen

##### New member
Drakmeire said:
Neither, you can't divide 0 by 2 or any other number.
Do I win?
You can divide zero by two. The answer is zero. Nothing can be divided by zero but zero can be divided by anything giving an answer of two.

OT:

As previously stated, zero is considered to be an even number because two can go into it evenly.

#### RUINER ACTUAL

##### New member
Look at it more simply. You can't divide nothing between two groups evenly. Any number is even is you try hard enough. 1 is even if you have two halves. Zero is not.

#### Purple Shrimp

##### New member
Fagotto said:
Purple Shrimp said:
in terms of functions it's both. a function is even if f(x) = f(-x) and odd if f(-x) = -f(x), and f(x) = 0 satisfies both. I don't know if that necessarily carries across to the number but it'd make sense
Well that doesn't say much since that is true of any integer.
not at all; for example, if f(x) = 1 then it's not true that -f(x) = 1, so it isn't odd. (This, of course, counters your argument but reveals the enormous flaw in my reasoning which I've just realised, which is that any constant function is even, including odd numbers. consequently 0 isn't both odd and even and im dumb)

#### The Seldom Seen Kid

##### New member
Zero isn't a number, so it's neither even or odd. It's, by definition, nothing. (That's just my thoughts. I'm not a mathematician or anything.)

On the other hand, if you divide 0 by 2, there's no remainders, so it could also be pair.

##### New member
blaqknoise said:
Even. You can split it equally into two groups.
Bad math is bad. 1 can be split equally into two groups as well. .5 and .5

#### Klarinette

##### New member
Heathrow said:
Mathematicians are lazy and the only reason 0 is technically even is because it fits the oversimplified definition of parity.
Pow; what I was going to say, but much more straight forward.

#### Ulixes Dimon

##### New member
It's even because the number before and after it are odd #### Bon_Clay

##### New member
It is definitely an integer, and is even. Not that it really matters much.

#### blaqknoise

##### New member
blaqknoise said:
Even. You can split it equally into two groups.
Bad math is bad. 1 can be split equally into two groups as well. .5 and .5
....Well fuck...

#### AnOriginalConcept

##### New member
MaxPowers666 said:
AnOriginalConcept said:
It's even.

A number is even if it is divisible by 2 with no remainder.
I really hope you dont honestly believe that.
...Wikipedia [http://en.wikipedia.org/wiki/Parity_of_zero] agrees with me, sir.

#### Xannieros

##### New member
Let me Wikipedia that for you.

0 is the integer immediately preceding 1. In most cultures, 0 was identified before the idea of negative things that go lower than zero was accepted. Zero is an even number, because it is divisible by 2. 0 is neither positive nor negative. By some definitions 0 is also a natural number, and then the only natural number not to be positive. Zero is a number which quantifies a count or an amount of null size.

#### Paul Hearding

##### Creator of Pro-gamer Gauntlet
Zero is, in fact, even.

There are several ways to prove this.

First (as it's already been discussed), any even number is an integer that, when divided by two, will yield another integer.
0 / 2 = 0.

And yes zero IS an integer. The set of integers is all whole numbers, negative and positive: {...-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5...}

So, dividing by two yields zero, which IS an integer, therefor zero is even.

Also, to add to the pot, there are actually "degrees of eveness" in which some numbers can be 'more even' than others. This basically just means, how many powers of 2 can that number be divided by. For example, 12 would be "doubly even" as it is divisible by 2 and 4. Zero, would then be the most even number ever as it is divisible by ALL powers of 2!

Also, to throw a little abstract algebra into the mix, we can also show that zero is an even number here too. In abstract algebra, we know that the sum of any two even integers must also be even. 2 + 4 = 6 and 6 is even. But also, you have negative numbers to consider. -16 + 20 = 4 and 4 is even. Well, consider 2 and -2. Both are even and -2 + 2 = 0. So, by this definition, 0 must also be even.

(You can also make this same sort of argument with the sum of any two odds being an even).

*Math-rant over*

#### Lullabye

##### New member
Heathrow said:
zfactor said:
Um, yeah, you can. You just get zero. It is also by definition, even. http://en.wikipedia.org/wiki/Parity_of_zero
Yes, okay. But how do you tell two chunks of nothing divided into equal groups apart from one big bunch of nothing with a set of scales in it? For that matter, what if you have three equal groups of nothing?

Mathematicians are lazy and the only reason 0 is technically even is because it fits the oversimplified definition of parity.
6.
you can have two groups of 3, or 3 groups of 2.
zero is even, in that it can be split evenly.
And why are people stuck on the concept of nothingness? Think in terms of apples.
2 apples, 2 people. both people have an apple.
1 appl 2 people. 1 person has an apple(and wont share cus hes an asshole)
0 apples. 2 people. No one has apples.
all is fair and balanced and even.

#### drummond13

##### New member
0p3rati0n said:
To the technical standpoint it's neither. It does however have the "even feel" to it. Probably because it's between -1 and 1 which are odd so our brains create it as an even although it's not.
Um, no. To the "technical standpoint" it's even. Not because it has an "even feel" to it. It actually is even.

#### gmaverick019_v1legacy

##### New member
Zantos said:
Custard_Angel said:
Neither... Zero is not an integer.

The concept of even and odd only applies to integers therefore 2 is even, 3 is odd, 3.5 is neither and 0 is neither also.
Actually zero is an element in the set of integers (the Z set).

Strictly speaking it's even, since when you do set mappings you use 2*n for evens and 2n+(or -)1 for odds where n is an integer. However the principle of odd and even is only really used in natural number mappings, and 0 is not a natural number. So essentially from an analytical maths perspective it doesn't really matter but for the sake of completeness it's even.
agree with this, depends on the perspective but alot of people seem to go the "n" route, so i will call it even based on that .

Even.

#### Benmonkey7

##### New member
blaqknoise said:
blaqknoise said:
Even. You can split it equally into two groups.
Bad math is bad. 1 can be split equally into two groups as well. .5 and .5
....Well fuck...
Actually, blaqknoise was correct. Dividing one by two gets you a fraction. In order for something to be even, dividing it by two has to equal an integer. One half is not an integer. But zero is an integer. 0/2 equals 0, which is an integer. So, 0 is even.

#### poppabaggins

##### New member
the lack of math knowledge here is appalling.

zero is even
proof by definition:

Even = {2*n : n is an integer}
0 is an integer (by the definition of the set of integers)
therefore, 0 is a real number (the set of integers is a subset of the set of real numbers)

2*0 = 0
0 is even QED

this site has a fairly multinational userbase, and I have counted answers both correct and incorrect from 3 separate countries. so much for "stupid americans" and their bad math skills.