is 0 even or odd?

[Redingold]

Actually, according to mathematics - it depends. There is no rule saying whenever 0 is a natural number or not. I's something that can be argued back and forth when people are bored and neither answer is wrong nor right.
Since to speak about a number being even or odd the number has to be considered a natural number, it all depends whenever you see 0 as natural or not.

No, the number in question must be an integer. 0 is definitely an integer.

 

[Flaming Geek]

The only real excuse people have for calling 0 not a number is that they say it is nothing. They say this based on "philosophy". Well, here's some philosophy for ya.

What is a number?

A number is a representation of a concept. (SOME concepts, not ALL concepts, so don't get snippy on the wording)

Nothing is the concept, 0 is the number representing that concept, you have to keep that straight in your head.

Once you have that straight, yes, 0 is even.

 

[savandicus]

So much fail in this thread, Here is how to do maths people. PROVE YOUR ANSWERS with proper definitions.

Here is the definition of the sets even and odd

Even = (2k : For any k exsisting in Z)
Odd = (2k+1 : For any k exsisting in Z)

Taken straight from wikipedia and also common sense states that this is the definition. A number is even or odd depending on which set it falls into. For those of you who dont know the set of Z is the set of all integers i.e (Z = (.... -2, -1, 0, 1, 2,...). Therefore k can have a value of 0 and therefore the even set contains the element zero.

Therefore zero is even.

FACT.

 

[Lukeje]

Actually, according to mathematics - it depends. There is no rule saying whenever 0 is a natural number or not. I's something that can be argued back and forth when people are bored and neither answer is wrong nor right.
Since to speak about a number being even or odd the number has to be considered a natural number, it all depends whenever you see 0 as natural or not.

Why does a number have to be a natural number to be considered even or odd?

 

[KingsGambit_v1legacy]

Yes, okay. But how do you tell two chunks of nothing divided into equal groups apart from one big bunch of nothing

The first group of nothing says the second group of nothing is dressed like a tramp and the second group of nothing says the first group is a 'ho.

And to let everyone know, I just divided by zero. That's how I roll.

 

[JMeganSnow]

Neither, you can't divide 0 by 2 or any other number.
Do I win?

You can divide zero by anything, it just equals zero. You can't divide numbers BY zero.

 

[Yopaz]

Neither.... zero is not a number, but a lack there of.

Wait, what?
Zero is not like darkness (being the absence of light).

Zero is a number like any other, and it is even.
Source: http://mathforum.org/library/drmath/view/57104.html

Thank you sir. I hate people who say zero is not a number! It annoys me so much you wouldn't believe it! Thanks for stating this and giving a source I can use of this ever comes up again. Right into my bookmarks this go. Also don't mistake my enthusiasm for sarcasm, I am genuinely happy to have this knowledge.

OT: It's even like the source from this guy says it is.

 

[The_root_of_all_evil]

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

0 is the most even of even numbers.

Although it originally wasn't on the number line. The Romans had no symbol for it. It's actually Arabic.

 

[anima110]

its even as any number ending in 0 is even as it is with 2,4,6 and 8

 

[Feste the Jester]

But since it isn't in the category of Real Numbers, it does not matter

0 is a real number. Nonreal numbers are those dealing with i.

OT: 0 is even because its divisible by 2 (without any fractions of remainders).

 

[Fitzcaraldo]

I'm not really sure... but it raises the question: Is infinity odd or even?

 

[Tzekelkan]

Here, all you armchair philosophers, read line 6, page 125, chapter 14 of Betrand Russel's Principles of Mathematics :

http://books.google.com/books?id=63ooitcP2osC&pg=PA125#v=onepage&q&f=false

Now cut it out! You can't say zero "isn't", because it totally is. It's a number, it's not an abstract representation of nothingness, not more than the fact that one(1) is the abstract representation of somethingness. See how I had to make up a word just to say that? That's how you sound like.

When you will have written a book on mathematics, you will get a say in what is or isn't this or that mathematical notion.

 

[Tzekelkan]

I'm not really sure... but it raises the question: Is infinity odd or even?

No, it does not. Zero is not the same as infinity. Zero is an integer, which means it's a real number. Infinity is not a real number, as in, it does not belong to R, the group of real numbers. It's similar to asing whether i is even or odd, not similar to whether zero is.

 

[Tzekelkan]

double post

 

[rutger5000]

Neither, you can't divide 0 by 2 or any other number.
Do I win?

You're wrong 0 is perfectly dividable by 2, you even get an integer value. Namely 0. So no you don't win. But you're conclusion might be right, 0 might not be even or odd. I'm tending to even, but I don't know for sure.

 

[Glademaster_v1legacy]

Zero is an even number. In other words, its parity?the quality of an integer being even or odd?is even. Zero fits the definition of "even number": it is an integer multiple of 2. As a result, zero exhibits the properties shared by all even numbers: 0 is evenly divisible by 2, 0 is surrounded on both sides by odd integers, 0 is the sum of an integer with itself, and 0 objects can be split into two equal groups. Zero fits into the rules for sums and products of even numbers, such as even − even = even, so any alternate definition of "even number" would still need to include zero. Within the even numbers, zero plays a central role: it is the identity element of the group of even integers, and it is the starting case from which other even natural numbers are recursively generated. Every integer divides 0, including each power of 2; in this sense, 0 is the "most even" number of all.

This is what google and wiki and things like Yahoo answers are for. Come on people stop being so lazy. I mean really it is not some abstract concept we are not talking about imaginary numbers here this is a real(budum tish) number stop saying it isn't.

 

[Sovvolf]

Well, google says even, wiki says even and the people on here that seem to have a very firm grasp of maths (I think we have some college students studying maths and some maths teachers) say its even.... So I'd say its even.

 

[FamoFunk]

I don't know. But it 'looks' like an even number, nothing odd about it.

 

[SL33TBL1ND]

Neither, you can't divide 0 by 2 or any other number.
Do I win?

You can, but you get 0. Splitting nothing into 2 equal parts is still nothing.

Neither, you can't divide 0 by 2 or any other number.
Do I win?

You can divide zero by anything, it just equals zero. You can't divide numbers BY zero.

Actually you can, but you get infinity or negative infinity, depending on whether you're approaching 0 from the positive or negative side. That's what a hyperbola represents.

Spoiler: y=1/x

 

[4li3n]

It's a number, it's not an abstract representation of nothingness,

Numbers are an abstract representation of something... so is math actually...


The reason ppl are confused about the issue is that you can't split nothing in two in any physical sense.


Why is it that most people that have studied pure math can't seem to remember that in the real world those numbers actually do represent some physical entity or force? Which is why Achilles and the tortoise is a paradox, because the logic of the proof if fine, but a human can overtake a turtle in the real world.


0 is even because it fits the definition, but i do wonder, would it ever even come up in the real world?