Is 0 even? (1 Viewer)

[currysauce]

Is 0 an even number?

Yes. An even number leaves no remainder when divided by 2. So, 0/2 = 0 and has no remainder. Also, an integer 'n' is called "even" if there exists an integer 'm' such that n=2m, and n is called "odd" if n+1 is even. Thus, 0 is even by this criterion as well.

Kool huh.

 

[Sober]

I appologise but do not share your awe in the discovery of this fact, it seems common sense to me.

 

[nick1048]

pretty cool... I'm not a maths person tho...

*stares @ sobers graph sig*

 

[Riviet]

Quite an interesting point you have there.

I have nothing to argue.

 

[sando]

well, noone ever thought it was an odd number

 

[YBK]

I asked my teacher that question a few weeks ago and I'm pretty sure she said neither even or odd.

Edit: Okay, I'm not too sure she said that now.. lol

 

[foobar]

Is 0 even?

No, because it's a meaningless question. It's a number, but division here is undefined. It's a special case, because you can't divide nothing.

 

[Dougie]

Is 0 even?

No, because it's a meaningless question. It's a number, but division here is undefined. It's a special case, because you can't divide nothing.

u can divide 0 by any number, u just can't divide by 0.

 

[foobar]

u can divide 0 by any number, u just can't divide by 0.

How does that make logical or mathematical sense?

Then answer: take zero, or nothing. Zip, nada, zilch. How many times does 10 go into zero? Prove your answer.

It's a meaningless question.

Edit: maybe the answer for all numbers is 0, since nothing can go into zero. But here we still have the problem of needing an even divide with no remainder. Nonsensical? Makes no logical sense to me.

 

[Dougie]

agree it's a meaningless question, and i don't like maths enough to really care if it's odd or even. But what i meant was...

how many groups of 5 can u take from 10, 2.
how many groups of 0 can u take from 10, 0.
how many groups of 10 can u take from 0, IMPOSSIBLE!

 

[foobar]

how many groups of 10 can u take from 0, IMPOSSIBLE!

I agree, in which case it is clearly not even. Makes me wonder about the basic or logical foundations of mathematics a lot. On the subject, I've posted a thread about Prof. Wildberger's Set Theory: Should You Believe? which is far more interesting, maybe even for those not especially interested in maths.

 

[Dougie]

not argueing whether it is or not, argueing the fact a number can't b divided by zero, which it can't.

eg. 10/0 not possible

 

[housemouse]

zero divided into zero is possible

 

[Xayma]

not argueing whether it is or not, argueing the fact a number can't b divided by zero, which it can't.

eg. 10/0 not possible

The ability to be divided by a number is irrelevant to the question about whether 0 is even.

0 ≡ 2 (mod 2)

As 2 is even, 0 is even.

zero divided into zero is possible

It is undefined.

 

[Sober]

The ability to be divided by a number is irrelevant to the question about whether 0 is even.

0 ≡ 2 (mod 2)

As 2 is even, 0 is even.



It is undefined.

It is a little stickier than undefined it is indeterminate. This means it may have a value in some contexts with more information.

 

[Forbidden.]

0 means nothing ... Anything divided by 0 is nothing ... It cannot be anything, let alone even or odd ... nothing = 0 (equals zero, not a face)

 

[Forbidden.]

" Zero is divisible by any number and leaves no remainder. In this it is unique. ( 0/n = 0 ; independent of what "n" is. When a number...say 5, is divided by a pedestrian integer you get quotients like: 1.666 (5/3) or 0.625 (5/8) but divide any number by zero and the quotient is...undefined. Every single time."

That's what some professor or something said. I don't really care if 0 is odd or even. It has no real bearing on anything.

That's what I was trying to explain ..

Is it my computer or has LottoX's sig disappeared ?

 

[Riviet]

Is it my computer or has LottoX's sig disappeared ?

I think it's just your computer.

With respect to the topic, my understanding of even numbers in relation to 0 is not enough to take a side.

 

[acmilan]

Whether 0 is even basically comes down to how you define divisibility. If you define a number being even meaning it is divisible by 2 and has any integer quotient, then 0 is even. I've never seen any reason at all to not include 0 as a possible quotient, so why would you? All saying 0 isnt even does is cause more restrictions to number properties. For example, adding even numbers gives an even number - saying 0 isnt even means you'd have to say something like 'the sum of even numbers is even, except when adding two numbers that are exact opposites'.

So, you see, there IS valid reason to say 0 is even.

 

[Templar]

No, because it's a meaningless question. It's a number, but division here is undefined. It's a special case, because you can't divide nothing.

In mathematics, to divide a number by n is defined as multiplying by its inverse. Every number apart from 0 has an inverse (either axiom or derived, can't remember for sure).

From axiom, there exist a number 0 such that 0*m=m*0=0.

Hence for all n not equal to 0, let m be the inverse of m, 0/n=0*m=0 by axiom.