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Is 0 an odd or an even number....

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Is 0 an odd or an even number?
0 is Odd 0%  0%  [ 0 ]
0 is Even 89%  89%  [ 34 ]
Do you expect me to know? 11%  11%  [ 4 ]
Total votes : 38

kxmode
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22 Jun 2009, 8:54 pm

It is neither. It is the absence of value.


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Kenjuudo
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22 Jun 2009, 9:34 pm

No, it's not. That's a common misconception.


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Saspie
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22 Jun 2009, 11:00 pm

http://en.wikipedia.org/wiki/Evenness_of_zero

Edit: Woops, missed seeing this posted already. What Michjo said :)



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23 Jun 2009, 8:33 am

Kenjuudo wrote:
Both of you fail to see that the value 0 is not a physical value, but a mental approximation, or thought experiment if you will, about the concept of nothing (even if "nothing" doesn't exist). It's a mentally constructed model. Just like the math generally isn't trying to describe nature exactly which is impossible anyway, but is a tool to describe nature as closely as possible. In nature, there are actually no numbers at all. No zeros, no ones, no twos. They are just intellectual tools, or attributes, we apply to nature to create order in the apparent chaos.


I am delighted to see someone else pointing this out.


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ruveyn
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23 Jun 2009, 8:53 am

sqoouf wrote:
I've been having this arguueament with a teacher since I was first Dx'ed.....
Is 0 an odd or an even number?


0 is even. When divided by 2 it leaves a remainder of 0. End of story.

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23 Jun 2009, 8:56 am

0 == 0 mod 2

The definition of an even/odd numbers is:

x is even if and only if x == 0 mod 2. x is odd if and only iff x == 1 mod 2.

In general for any divisor n (not = 0) x == r mod n for some value of r between 0 and n-1

note: == is the modular equivalence defined by Gauss.

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23 Jun 2009, 10:40 am

i would say "zero" is a numeral and not a number. (and i just did)
there can not be said to be a "number" of things if there are no things.

i think the concept of "number" values arose from ancient market places, and if you had no apples, then that was 1 less apple than having one apple.

so the "number line" starts at 0 and proceeds endlessly upward.
then it was considered that there can be numerals that are less than zero because in their accounting back then, the subtraction of a "greater" from a "lesser" introduced a notional deficit, and that was something to be addressed.

i am happy with our number system, even though i think that a number system that starts from zero (nothing) is an illusion.
"nothing" is not in existence, and nothing can originate from there. no multiples of zero will ever result in any reality.

when i was little, i thought it would be better to subdivide infinity rather than multiply zero when thinking about number sequences.

but if you split infinity in half, then you have infinity. and you can split that in half forever and never achieve any other result than infinity.

same as multiplying zero by zero.

how can zero ever get to 1 by multiplication? it can never. double zero for ever and there is still nothing.

the only way the number line can get started is by addition of a supposed value, and that is not the most efficient way to start off a mental frame in my mind.

so to ask a question about the divisibility by 2 of a point that does not exist is not valid in my mind.

i say "0" is neither odd nor even. it is simply not.



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23 Jun 2009, 10:54 am

b9 wrote:
i would say "zero" is a numeral and not a number. (and i just did)
there can not be said to be a "number" of things if there are no things.

i think the concept of "number" values arose from ancient market places, and if you had no apples, then that was 1 less apple than having one apple.

so the "number line" starts at 0 and proceeds endlessly upward.
then it was considered that there can be numerals that are less than zero because in their accounting back then, the subtraction of a "greater" from a "lesser" introduced a notional deficit, and that was something to be addressed.

i am happy with our number system, even though i think that a number system that starts from zero (nothing) is an illusion.
"nothing" is not in existence, and nothing can originate from there. no multiples of zero will ever result in any reality.

when i was little, i thought it would be better to subdivide infinity rather than multiply zero when thinking about number sequences.

but if you split infinity in half, then you have infinity. and you can split that in half forever and never achieve any other result than infinity.

same as multiplying zero by zero.

how can zero ever get to 1 by multiplication? it can never. double zero for ever and there is still nothing.

the only way the number line can get started is by addition of a supposed value, and that is not the most efficient way to start off a mental frame in my mind.

so to ask a question about the divisibility by 2 of a point that does not exist is not valid in my mind.

i say "0" is neither odd nor even. it is simply not.
As I said, this is a common misconception, even though it's more prevalent in children than in adults. You may very well think of 0 as "not", but that doesn't mean it's correct. Mathematically, 0 is a perfectly valid number and can be proven as such. Please read the article that was linked to twice in this thread.


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Dilbert
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23 Jun 2009, 12:09 pm

This group, of all people, should know that science is supposed to be about facts, and not beliefs or conjecture or idle speculation (although much good science has emerged from the latter two!) Read my last post. Zero IS an even number. That is not open for discussion. And dividing by zero is certainly possible. Result is infinite. (Except dividing zero by zero.)



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24 Jun 2009, 3:11 pm

Zero is an even number for the reasons given by previous posters.

Dilbert wrote:
Zero is an even number.

A number (other than zero) can be divided by zero. Result is infinity.

X/0=∞

However zero can't be divided by zero! Result is undefined.

0/0=N/A


When dividing a non-zero number by zero the result is infinity if you use the concept of limits. More precisely:

X/Y approaches ∞ as Y approaches 0

-X/Y approaches -∞ as Y approaches 0

The situation of 0/0 is actually indeterminate because it can approach any number you like depending on the situation. As an example:

(X^2 + 4X + 3)/(X+1) is a case of 0/0 if you take X = -1 however if you take the limit of X approaching -1 the answer is actually 2 (factorize the numerator and a factor of (X+1) cancels in the top and bottom, then substitute -1 afterwards).



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24 Jun 2009, 3:12 pm

I am guessing that it's neutral.



EtotheC
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24 Jun 2009, 4:46 pm

Humanity defines the definition of what "Odd" and "Even" are, due to the nature of language "0" could just as easily be defined as Pi.This is simply answered with the statement: it is what humanity makes it.



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24 Jun 2009, 4:51 pm

Probably true, but humans defined '0', 'even' and 'odd' in the same context. Zero is defined to be even. There is no more to discuss. ;)


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24 Jun 2009, 8:50 pm

It's neither. It's not positive or negative, either. :-P
The concept of zero is actually fairly recent.. You'll notice that there's no way to represent zero in Roman numerals.. Europe had pretty much no concept of zero until it adopted Arabic numerals.



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24 Jun 2009, 9:12 pm

Maggiedoll: You are right in that zero is neither negative or positive. But it is an even number regardless.

Guys, this needs to be the end of the discussion. Here's the actual definition:

mathforum.org wrote:
An integer n is called *even* if there exists an integer m such that n = 2m, and *odd* if n+1 is even. From this, it is clear that 0 = (2)(0) is even. The reason for this definition is so that we have the property that every integer is either even or odd.


And this was used to explain it to a child:
mathcentral.uregina.ca wrote:
A number is even if it is divisible by 2 without a remainder. So 6 is even since 6 divided by 2 is 3, and 12 is even since 12 divided by 2 is 6, but 7 is not even since 7 divided by 2 is 3 with a remainder of 1. What about zero? Zero divided by 2 is zero with no remainder so zero is even.


Stop confusing people by saying it's neither. That's wrong!


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pakled
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26 Jun 2009, 11:50 pm

Every time my computer divides by zero, it locks up. It even tells me...;)

I think 0 is a mental construct. It's not much of a number. When used as a placeholder, it's always even, but ....who cares?...;)

But I've never worried about it...;)