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Parity of zero

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This peer review discussion has been closed.
I've listed this article for peer review in order to polish it for a FAC. I ran the article through a peer review and a failed FAC a few years ago, and I've implemented a lot of feedback since then. (See the talk page and especially the links in the "Article milestones" template.) Feedback of any kind toward any part of the article is welcome!

Thanks, Melchoir (talk) 05:35, 7 June 2013 (UTC)[reply]

Comments from Trovatore

I recall one person who thought the question was more problematic than for nonzero integers, on the grounds that nonzero integers have unique factorizations into primes, and you can check whether a nonzero integer is even or odd simply by noticing whether 2 appears in the factorization. For 0 that doesn't work.

I don't know whether this argument has come up in the studies of people's views, but if it's sourceable it might be interesting to add. In this connection, it may be a problem that the article currently claims that "numbers have unique factorizations" but fails to note that 0 in fact does not. --Trovatore (talk) 19:04, 12 June 2013 (UTC)[reply]

Hmm, unfortunately I haven't seen that idea mentioned in studies of people's views. We can still make sure it's covered in the "Mathematical contexts" section. I just wouldn't want to list it as a reason for why some people that believe zero isn't even.

I've edited the article to say that positive numbers have unique factorizations[1] and zero doesn't have one[2], which is why its 2-adic order is a special case. Melchoir (talk) 23:03, 12 June 2013 (UTC)[reply]