Is zero odd or even?

Answer 1

Well, some people are right, some are wrong, but it's really not about dividing. Division is just a run around. Here's the real definition of even numbers, which is what we should always appeal to:

An even number is a INTEGER MULTIPLE OF TWO:

-4 × 2 = -8
-3 × 2 = -6
-2 × 2 = -4
-1 × 2 = -2
0 × 2 = 0
1 × 2 = 2
2 × 2 = 4
3 × 2 = 6
4 × 2 = 8
etc...

Integers: -4, -3, -2, -1, 0, 1, 2, 3, 4
Evens: -8, -6, -4, -2, 0, 2, 4, 6, 8

Notice how they match up.

You can also try to remember that evens (and odds) skip by 2s. So odds go:
1+2=3
3+2=5
5+2=7

evens go:
2+2=4
4+2=6
6+2=8

But you can also count back in 2s:
8-2=6
6-2=4
4-2=2
2-2=0

Look, 0 is even.

An even number is any number that can be written as 2 times some integer. 18 is even:

18 = 2 × n (for this one, n = 9)

0 = 2 × n (for this one, n = 0)

Answer 2

Even numbers have the form 2n, where n is an integer.
Odd numbers have the form 2n + 1.
By that definition, zero obviously is even (n=0). No value of n will make 2n+1=0, so zero is certainly not odd.

Now think of some properties of odd and even numbers, and think of what would happen to them if zero were not even:

- The sum of two odd numbers is even. 1+3=4. (-9)+5=(-4). Well, what about 7+(-7)=0? Does the rule haev to be changed to "The sum of two odd numbers is even, unless that sum happens to be zero?"

- Even and odd numbers alternate - An odd number (e.g. 3) is always preceded and succeeded by an even number (2 and 4). Do we make an exception to that rule for 1 and -1?

And on and on... If we treat zero like any old ordinary EVEN number, these rules work fine and don't need any exceptions made. If we make an exception out of zero for no good reason, all we do is introduce exceptions to the above rules for no good reason.

So Zero is even and there is Zero controversy about this among mathematicians... but seeing how many people have a hard time wrapping their head around this, I conclude that Zero must be a very odd number indeed!

Answer 3

Zero is even. (I am not really sure why some people seem to think it is neither odd nor even.)

An integer is even if, when you divide it by two, you get an integer.

Zero divided by two is zero, which is an integer. So zero is even.

If you don't like that argument, think about what being even means: A number is even if it can be written as the sum of an integer with itself. For example,

8 is even, because 8 = 4 + 4
76 is even, because 76 = 38 + 38
-12 is even, because -12 = -6 + (-6)

and also

0 is even, because 0 = 0 + 0

If you don't like that argument, then look at the odd integers other than zero and the even integers other than zero:

Even: ..., -10, -8, -6, -4, -2, 2, 4, 6, 8, 10, ...
Odd: ..., -9, -7, -5, -3, -1, 1, 3, 5, 7, 9, ...

It certainly looks like 0 is even here, doesn't it?

Answer 4

Number Theory says that "the sum of two odd numbers is an even number." By that definition, zero is an even number.
Consider: -1 + 1 = zero, which is the sum of two odd numbers.
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Show that the sum of two odd numbers is an even number.

Solution

Let 2n + 1 and 2k + 1 be the odd numbers to add. The sum of the two numbers is given by

(2n + 1) + (2k + 1) = 2n + 2k + 2 = 2(n + k + 1)

Let N = n + k + 1 and write the sum as

(2n + 1) + (2k + 1) = 2N

The sum is an even number.
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OTHER DEFINITIONS

An even number is any integer divisible by 2.

Example: ...-4, -2, 0, 2, 4, ...

Consider: zero / 2 = zero <-- even

Any even number may be written as a multiple of 2 as

2n

Consider: 2 x Zero = Zero <-- even

An odd number is any integer not divisible by 2.

Example: ...-5, -3, -1, 1, 3, ...

Any odd number may be written as

2n+1

Consider: (2 x Zero) + 1 = (zero) + 1 = 1 <-- odd
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OTHER PROOFS:
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Show that the sum of two even numbers is even.

Solution

Let 2n and 2k be the two even numbers. The sum of the two numbers is written in factored form as follows

2n + 2k = 2(n + k)

Let N = n + k and write the sum as

2n + 2k = 2N

The sum is an even number.

Consider: -2 + 2 = zero <-- even

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Show that the sum of an even number and an odd number is an odd number.

Solution

Let 2n be the even number and 2k + 1 be the odd number. The sum of the two numbers is given by

(2n) + (2k + 1) = 2n + 2k + 1 = 2(n + k) + 1

Let N = n + k and write the sum as

(2n) + (2k + 1) = 2N + 1

The sum is an odd number.

Consider: 2 + 1 = 3 <-- odd

Answer 5

Even. According to these guys.

"Zero is an even number. An even number is a number that
is exactly divisible by 2. That means that when you divide by two the remainder is zero."

Interesting question.

Check the source for better details

Answer 6

Zero fits the definition of an even number, since it yields an integer when divided by 2.

Who's the idiot giving all the correct answers a "thumbs down"?

Answer 7

Even, it is divisible by 2.

Answer 8

i withdraw my answer because of what she said

cipherdemon -


i only half understand and why it makes sence to a point - i sitll dont think you can divide zero by any number - it means that amount does not exist -

Answer 9

I'd say even, since one is an odd. I don't know mannn!

Answer 10

Even.