Discovery: Grammatical Group

While over a discussion with my linguist/awesome/web programmer friend Eric Akaoka, I discovered the most interesting thing.

He was going about correcting people on the proper use of the plural form of words, which is completely normal for him.
e.g.

Octopus -> Octopi
Uterus -> Uteri
Clitoris -> Clitorises

Clitoris turned out to be a bit confusing, since most people expected the plural to be Clitori, but Eric corrected us that it was, in fact, Clitorises. For it to be the way we expected, the word would have had to be "Clitorus" with the -us ending.

Suddenly it hit me.

I turned to Eric, and asked
"So, what's the plural of 'us' then?"

There was a few seconds of silence, and then we realized that we had discovered something beautiful:

The plural of I is US, and the plural of US is I. Mathematically speaking, {I, us} is a group under the "plural" operation.

So,

plural(I) = Us
plural(Us) = I

also, the product plural*plural is the identity operator.
i.e. plural(plural(I)) = (plural*plural)(I) = I

fantastic!