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Is zero odd or even?

Is $0$ an odd number?

$1$ is an odd number. $10$ is an even number.

NOTE: There's nothing in $0$ which can be divided to check for evenness or oddness.

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marked as duplicate by sdcvvc, Cameron Buie, Brian M. Scott, Jennifer Dylan, mixedmath Aug 22 '12 at 16:30

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$0$ is an even number. –  Alex Becker Aug 22 '12 at 16:21
Count backwards by $2$'s: $\dots, 6, 4, 2, 0, -2, -4,\dots$. These are all even. –  André Nicolas Aug 22 '12 at 16:25
You can divide $0$ by anything you want (except by $0$...). Since $\frac{0}{2} = 0$ is an integer, $0$ is even. –  Joel Cohen Aug 22 '12 at 16:26
Why all the down-votes? –  Michael Hardy Aug 22 '12 at 18:41
@MichaelHardy The original form of the question was very poor, hence my downvote. It might contribute that a number of users are probably fed up with the consistently poor questions this user has asked. –  Alex Becker Aug 23 '12 at 2:23

2 Answers 2

up vote 5 down vote accepted

$n$ is even iff $n \equiv 0 \pmod{2}.$ $n$ is odd iff $n \equiv 1 \pmod{2}.$

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A number is even if the remainder after dividing by $2$ is $0$. The remainder of $0$ after dividing by $2$ is clearly $0$, so it is even.

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@RajeshKSingh It doesn't matter what's "in" $\,0\,$ (whatever that means). The definition of an even number is any number that is congruent to $\rm\, 0\ mod\ 2$. –  Arkamis Aug 22 '12 at 16:29
You don’t even have to think in terms of division. An integer $n$ is even if and only if there is an integer $m$ such that $n=2m$. $\ 0$ is an integer, and $0=2\cdot0$, so $0$ is even. –  Brian M. Scott Aug 22 '12 at 16:32
@RajeshKSingh You can divide $0$ by $2$, it gives you $0$. Thus the remainder is $0$. Thus it's even. –  Alex Becker Aug 22 '12 at 16:32
there's nothing in $0$, unlike $1$,$2$,$3$,$\ldots$ –  Rajesh K Singh Aug 22 '12 at 16:36
@RajeshKSingh "there's nothing in 0" doesn't mean anything. You're speaking gibberish. –  Alex Becker Aug 22 '12 at 16:37

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