sniffnoy | Sleep is still good

First off, a problem Chris posed to us today, saying he got it from Dr. Nevard (so Chris doesn't know the solution either.):

R is a ring with identity st ∀a∈R, a⁴=a. Prove R is commutative.

We thought we had proven cancellation (which would certainly make things easier (though in fact we didn't get it with that either)), then we realized our proof was circular. Ugh.

I'm sure someone out there is laughing his head off at how easy this actually is. Or perhaps not. CounselorJosh hasn't been able to solve it yet, I know that.

I got out of bed at 13:50 today, missing both breakfast and lunch. I went to Burger King and got a cheeseburger instead; then, for dinner, I ate cereal. (Don't ask.)

I played my first game of Diplomacy last night, though we didn't finish it. (We only went till Fall '03.) More specifically, we didn't even record it to continue it later, so we *really* won't finish it. Oh well.

-Sniffnoy

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"Directional microphones don't make very good phasers, do they?"
-Grenadier