Some people say that 0 is neither even nor odd. I say that 0 is even.
Is there a simple way to convince people that 0 is even and the statement that "0 is neither even nor odd" is false.
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Most people who practice mathematics regularly take $0$ to be an even integer, since it is divisible by $2$: $2 \times 0 = 0$. Furthermore, taking $2$ to be even makes a lot of statements a lot more concise. Call it odd, call it even if'n ya wanna, but I vote for $2$ *even*!!! Cheers! – Robert Lewis Apr 04 '15 at 04:20
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2http://en.wikipedia.org/wiki/Parity_of_zero – Todd Wilcox Apr 04 '15 at 04:21
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"Believe"? This is mathematics, not some touchy-feely subject like poetry. – Jonathan Hebert Apr 04 '15 at 04:22
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@JonathanHebert: Sorry, "think" is better? – user172675 Apr 04 '15 at 04:24
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1@JonathanHebert That is hardly necessary here. – Daniel W. Farlow Apr 04 '15 at 04:24
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1@JonathanHebert: how in heaven's name did you come with the notion that poetry is a "touchy-feely" subject? – Robert Lewis Apr 04 '15 at 05:47
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An integer, $x$, is defined to be even whenever it can be written in the form $x=2k$ where $k$ is some integer.
Examples: $6=2\cdot 3,~~ 10 = 2\cdot 5,~~ 2218 = 2\cdot 1109,~~ -4 = 2\cdot (-2)$
An integer, $x$, is defined to be odd whenever it can be written in the form $x=2k+1$ where $k$ is some integer.
Examples: $-3 = 2\cdot (-2) + 1,~~~ 9 = 2\cdot 4 + 1,~~~ 1001 = 2\cdot 500 + 1$
Remember that $0$ is itself an integer, and that $0 = 2\cdot \color{red}{0}$, which is in the form $0=2k$ with $k = \color{red}{0}$, therefore $0$ is even.
JMoravitz
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@user172675 This is hardly a proof--if someone accepts that $0$ is actually a number, furthermore an integer, then the fact that $0$ is even is a trivial conclusion. Your question is far more philosophical than you may think, for the concept of zero goes way way back. – Daniel W. Farlow Apr 04 '15 at 04:28