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 Post subject: Is zero an even number?Posted: Thu Jul 17, 2014 7:24 pm

Joined: Mon Feb 22, 2010 2:50 pm
Posts: 640
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?

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 Post subject: Re: Is zero an even number?Posted: Thu Jul 17, 2014 7:46 pm

Joined: Tue Dec 18, 2012 10:59 am
Posts: 3579
Love this:
http://www.bbc.co.uk/news/magazine-20559052
I know you have googled, but you sparked my interest and I liked this good old BBC report the best.

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 Post subject: Re: Is zero an even number?Posted: Fri Jul 18, 2014 9:25 am

Joined: Mon Feb 22, 2010 2:50 pm
Posts: 640
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.

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 Post subject: Re: Is zero an even number?Posted: Fri Jul 18, 2014 9:38 am

Joined: Sat Jul 21, 2012 5:55 pm
Posts: 375
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.

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 Post subject: Re: Is zero an even number?Posted: Fri Jul 18, 2014 9:48 am

Joined: Mon Feb 22, 2010 2:50 pm
Posts: 640
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.

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 Post subject: Re: Is zero an even number?Posted: Fri Jul 18, 2014 1:37 pm

Joined: Thu Nov 22, 2007 10:30 am
Posts: 531
Location: Warwickshire
It's not that long ago that zero wasn't considered a number at all...

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 Post subject: Re: Is zero an even number?Posted: Sat Jul 19, 2014 10:04 am

Joined: Fri Jul 18, 2014 9:18 am
Posts: 6
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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