Is zero an even number?

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Hera
Posts: 856
Joined: Mon Feb 22, 2010 3:50 pm

Is zero an even number?

Post by Hera »

This has come up in the Bond Test Papers 1. The answer assumes that 0 is not an even number. I have searched on the web and there seems to be some debate. What do people think?
southbucks3
Posts: 3579
Joined: Tue Dec 18, 2012 11:59 am

Re: Is zero an even number?

Post by southbucks3 »

Love this:
http://www.bbc.co.uk/news/magazine-20559052" onclick="window.open(this.href);return false;
I know you have googled, but you sparked my interest and I liked this good old BBC report the best.
Hera
Posts: 856
Joined: Mon Feb 22, 2010 3:50 pm

Re: Is zero an even number?

Post by Hera »

Thanks southbucks. I think it should be classed as an even number and the bond exam paper is wrong or at least it is a silly question when it is debatable.
Jean.Brodie
Posts: 451
Joined: Sat Jul 21, 2012 6:55 pm

Re: Is zero an even number?

Post by Jean.Brodie »

Hera:

'An even number is an integer which is "evenly divisible" by two. This means that if the integer is divided by 2, it yields no remainder. Zero is an even number because zero divided by two equals zero. Even numbers can be either positive or negative.'

Source: a well known online encyclopaedia.

The more important fact to remember is that ONE is not a prime number.
Hera
Posts: 856
Joined: Mon Feb 22, 2010 3:50 pm

Re: Is zero an even number?

Post by Hera »

Thanks JeanBrodie that was my understanding and I think the general if not overriding consensus. I was questioning it as there is some debate and it was not viewed as an even number on an 11+ paper.
Warks mum
Posts: 538
Joined: Thu Nov 22, 2007 11:30 am
Location: Warwickshire

Re: Is zero an even number?

Post by Warks mum »

It's not that long ago that zero wasn't considered a number at all...
lauren85
Posts: 6
Joined: Fri Jul 18, 2014 10:18 am

Re: Is zero an even number?

Post by lauren85 »

The usual definition of "even" and "odd" is just that for any integer k (integer = the whole numbers, negatives, and 0), the number 2k is "even" and the number 2k+1 is "odd". 0 is even since 0 = 2*0. These are precisely the equivalence classes in the integers modulo 2, formally written as Z/2Z [actually the Z's should be in blackboard bold, but whatever].

If you ask a bunch of mathematicians, virtually all of them will say that 0 is even. None of them would ever say that 0 is odd. You *might* find some that will say neither, but almost certainly not. One very nice property of even numbers is that adding arbitrary even numbers results in another even number. This property breaks if you don't consider 0 even, since (-2) + (2) = 0.


There's a small argument for not calling 0 even, which uses the following definition of "even":
An even number is an integer n where there is some integer m such that n/m = 2.
This definition includes all the usual evens, except that it excludes 0. I find this definition stupid for the reason above--addition of evens is then no longer closed. But, I can see where someone not trained in math could use either definition. I think the (even) + (even) = (even) property should be enough to convince anyone to call 0 even.
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