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I see commutivity used in contexts where the meaning appears to be the same as commutativity. Here are an example from physics and another example. Is commutivity incorrect? Does it differ from commutativity?

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I'm guessing these are simple misspellings. – GEdgar Mar 26 '12 at 14:11
I've never heard of commutivity. Even spell-checker marks it wrong. – user Mar 26 '12 at 16:07
I have up-voted your question, as I had often wondered about that myself:) – Hexagon Tiling Mar 27 '12 at 2:05

The correct form is commutativity (commutivity isn't listed in OED). Here's a usage chart showing that the incorrect form isn't used very often, so it doesn't seem likely to take over any time soon.

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Google gives you a pretty strong hint if you search for Rubin's commutivity principle - it says "About 2470 results" and asks "Did you mean: Rubin's commutativity principle". If you search for the suggested alternative instead, it produces "About 1,200,000 results". Case closed, I think.

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Right. The Commutative Law or Commutative Property are common in math, and the normal way to name a property after an adjective ending in -ive is with -ivity. But you still need that -ta- in front of the -tivity. – John Lawler Mar 26 '12 at 14:22
@John: It seems like all my life I've been slightly disorientated by the question of whether I should really be disoriented. Thanks to the power of Google Books, I now see that back when I was trying to get to grips with such things, British English was decidedly undecided on the matter – FumbleFingers Mar 26 '12 at 14:41
Is Google really the authority on correct English now? Is there an argument either way from a known, published language rule? Or is this a gray area? – Eli Rosencruft Mar 26 '12 at 15:09
@EliRosencruft: Google and NGrams is not an authority and it has its data collection problems and can't always be taken at face value (it counts whatever you ask; you need to ask things the right way). but it does give a good idea of how people tend to use things. People may make 'mistakes' more often than the 'correct' version, but simply by popularity the 'mistake' becomes 'correct'. But that's also a judgement call. – Mitch Mar 26 '12 at 15:18
@Eli Rosencruft: Before I made any reference to Google Books, I did point out in my answer that "commutivity isn't listed in OED". I then specifically added the results from a search for "Rubin's commutativity principle", on the grounds that people who had heard of that were more likely to be familiar with the correct spelling. The chart was partly to reassure OP that commutivity does in fact occur (albeit at a relatively low level), so his question wasn't completely ridiculous. – FumbleFingers Mar 26 '12 at 15:45

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