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Is zero even?
By Anne Pepper (T2093) on Friday, March 10, 2000 - 09:20 am:

Is zero an even number?
If you consider the pattern of other numbers that end in zero e.g. 10, 20 etc you would conclude it was even. If you consider the sequence of integers as 'every other one is even' then 4,2,0 you would conclude it was even. Yet if you use a divisibility rule such as 'can be divided into 2 equal, integer parts which are smaller than the number' then you would conculde it was not even, i.e. m is even if, m=2n, where n<m.
What do you conclude?

By Anonymous on Friday, March 10, 2000 - 02:08 pm:

If you define even as "the remainder is 0 if divided by 2" then 0 is certainly even. It really depends on the context, whether 0 should be considered as even or not (it is certailnly not odd).

By Anonymous on Friday, March 10, 2000 - 03:50 pm:

I think the above comment stands, but if you want to be really confused:

If 0 was the only number that was neither odd nor even by definition, it would certainly be odd, but then it would not be neither odd nor even, thus giving a logical paradox somewhat analogous to that of Bertrand Russell !

By Clare Nicholson (P1732) on Sunday, March 12, 2000 - 06:04 pm:

Ok totally confused by everything the one above's said.

Odd + odd = even
Even + even = even
Odd + even = odd.

So call the odd 1 and even 2.

1+1=2 (even) 2+2=4 (even) 1+2=3 (odd)

But 0+0=0(what were finding out.)
2+0=2 (even)
1+0=1 (odd)

Therefore 0 is a even number.

Also going back to primary school draw a pair of scales and draw two triangles on one size and two triangles on the other too. They are even.

Draw nothing on one side and nothing on the other they are still even.

0 is even.

Luv Clare Nicholson (13yrs)

By Dan Goodman (Dfmg2) on Wednesday, March 15, 2000 - 08:13 pm:

Here's another definition of even. m is even if m=2n for some integer n. m is odd if m=2n+1 for some integer n. So 0 is even as 0=2*0. 0 is not odd as 2*0+1=1 and 2*-1+1=-1.

By Clare Nicholson (P1732) on Thursday, March 16, 2000 - 06:16 pm:

Basically yes 0 is even but no it cn't be / by 2 and still be a whole number.

By Cathy Davies (P2201) on Thursday, March 16, 2000 - 07:11 pm:

if 0 isn't even (and it's definitely not odd), then what is it?

By Clare Nicholson (P1732) on Friday, March 17, 2000 - 11:02 pm:

0 is even!!!! And if ur defination off even is a number that can be / by 2 and still have a whole number then what about 0.2 isn't that even?. But then can minus numbers be equal?

Clare (13yrs)

By Monalisa Chati (P2218) on Sunday, March 19, 2000 - 09:17 am:

Acc. to the pattern 10, 20, 30 etc 0 is even.
But 1 and 3 are not even.
Now applying Clare's method :

odd + even = odd
we get that 0 is odd.---------------------1
But if we are to consider the sequence of integers, we find that 0 is even.------2

From 1 and 2 we find that 0 is odd as well as even.

By Jonathan Kirby (Pjk30) on Sunday, March 19, 2000 - 08:41 pm:

No, from the pattern

odd + even = odd

we don't get than zero is odd because we also have
that

even + even = even.

Hence this method can't be used to deduce whether
any number is odd or even.

In fact 0 is certainly even, and every integer is
either even or odd, but not both. The best
definition of an even integer is one that is 2
times any integer. e.g. 6 is even because it is 2
times 3 and 0 is even because it is 2 times 0. An
odd integer is any integer which isn't even. The
notion of a number being odd or even only works
for integers, not fractions or other sorts or
numbers.

(An integer is a whole number: positive, negative
or zero.)

I hope that this helps.

Jonathan

By Clare Nicholson (P1732) on Monday, March 20, 2000 - 07:00 pm:

Sorry,

I dunno how old you lot are but I'm only 13 and I'm pretty sure 0 is even. (And totally confused by some other messages)

x=x y=y 9=9 2=2 0=0

That might totally confuse everyone but basically draw (imagine) a pair of weighting scales put x on one side then put x on the other, are the scales equal? Yeah they are. Add them together you get 2x. (2 being equal)

Put 9 on one side and 9 on the other, are the scales equal? Yeah, add them together that makes 18 (another equal number)

Put any number you like on one side and put the same number on the other, this number may be odd or even. Are the scales equal? Yeah.

Now put 0 on one side and 0 on the other side, the scales are still equal. But that doesn't mean that 0 is even because as long as you had the same number on each side the scales would be equal weather the number be odd or even.

But the numbers added together equals an even number. 0+0=0 therefore zero is even (isn't it?)

Totally Confused

Clare

By Jonathan Kirby (Pjk30) on Monday, March 20, 2000 - 09:08 pm:

Clare,

You are absolutely correct. Your method for testing whether a number is
even or odd works, and your last explanation is entirely correct. If other
people (like me) have written things that are confusing then that's not your
fault!

Jonathan

By Clare Nicholson (P1732) on Tuesday, March 21, 2000 - 08:41 pm:

Thank you Jonathan I think I know what I'm talking about now. And when in my message I wrote a equal number I meant a even number.

By Joanna Cheng (P2322) on Thursday, April 20, 2000 - 05:45 am:

Clare
Yep, I agree with you in saying that 0 is even. But some of the other comments that said 0 is odd make sense too. And it can't be both, as an interger can only be either odd or even. Anyway, some of these comments have certainly started to make me think!
Joanna

By Yvonne Teng (P2396) on Friday, April 21, 2000 - 10:22 am:

i'm very confused by all these explanations! I think 0 IS even.

By Jonathan Kirby (Pjk30) on Friday, April 21, 2000 - 12:32 pm:

0 is even.

Almost all of the above arguments that suggest that 0 is odd are flawed in some way or other. Some of the flaws are quite subtle however, which means that we can learn from them. (Learning from mistakes is one of the important ways of learning in mathematics.)

The only argument that isn't flawed is the very first one given by Anne Pepper. She defined n to be even if it can be written as n = 2m where m < n. The only way to write 0 = 2m is to take m = 0, but 0 is not less than 0, so 0 is not even.

This is correct reasoning, but it is not a good definition of even, and it is not the one which is used. It's not good because the condition that m < n doesn't serve any useful purpose, and it makes 0 and all negative numbers not even which is unhelpful.

I hope that this clears up the confusion.

Jonathan Kirby

By Rachel Grant (P1159) on Sunday, April 30, 2000 - 05:36 pm:

I say Clare Nicholson is right. i'm only 13, and so the rest of your explanations are way too complicated. So I think 0 is even. Besides. THe pattern of odd/even numbers goes odd, even, odd, even, odd, even, etc. If 4 is even, 3 is odd, 2 is even, 1 is odd, it only makes sense for the pattern to go on and for 0 to be....even!

Thanks

Rachel

By Abhaya Agarwal (P2571) on Tuesday, May 30, 2000 - 10:49 pm:

Its ok that 0 is even but u should not say that .2 is even !! Even odd are defined only for whole no.
abhaya