Another property of the # operator, analogous to xor: It satisfies the rule (X#Y)#X = X#(Y#X) = Y. This is the rule for Semisymmetric Quasigroups, which I temporarily called Babagroups last year, and which Don Knuth calls Gropes. Incidentally, I received a couple of stone tablets from DEK this summer, mostly about Gropes. I'll get them transcribed here someday. Rich -----Original Message----- From: math-fun-bounces+rschroe=sandia.gov@mailman.xmission.com on behalf of Michael Kleber Sent: Thu 9/15/2005 7:08 AM To: math-fun Subject: Re: [math-fun] A ternary notation Eric Angelini wrote: <snip: base 3 stuff> Two particularly nice properties of trits are that (1) a single trit can hold a determination of <=>, and (2) there's a tritwise operation analogous to xor, well-known now as the rule of the award-winning children's card game "Set": if a=b, then a#b is a, and if a!=b, then a#b is the third state, c. (Or, a#b is -a-b mod 3, if you prefer.) --Michael Kleber (I'm suppressing an odd urge to include a middle name in my signature, to go with the rest of the 3-not-2 theme...) -- It is very dark and after 2000. If you continue you are likely to be eaten by a bleen. _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun