Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Posting-Version: version B 2.10.2 9/18/84; site brl-tgr.ARPA Path: utzoo!watmath!clyde!burl!ulysses!mhuxr!mhuxb!mhuxn!mhuxm!mhuxj!houxm!vax135!cornell!uw-beaver!tektronix!decvax!genrad!mit-eddie!godot!harvard!seismo!brl-tgr!gwyn From: gwyn@brl-tgr.ARPA (Doug Gwyn) Newsgroups: net.math Subject: Re: Beyond Exponention Message-ID: <8072@brl-tgr.ARPA> Date: Wed, 6-Feb-85 02:06:53 EST Article-I.D.: brl-tgr.8072 Posted: Wed Feb 6 02:06:53 1985 Date-Received: Sun, 10-Feb-85 06:40:27 EST References: <460@decwrl.UUCP> Organization: Ballistic Research Lab Lines: 18 > but like the 2 preceding functions a+b and a*b, a$b is both communitive > and associative, that is a$b==b$a and a$(b$c)==(a$b)$c. It also obeys > the distributive law, that is a$(b*c)==(a$b)*(a$c). If you want to get algebraic, observe that a*b is not a group (no inverse for 0) and in general one expects to lose an algebraic characteristic for each operation in the progression. This is a lot like the progression real -> complex -> quaternion. I don't think there is a single "right" answer to the question, "What operation is the third in the sequence +, *, ...?" any more than there is a single right answer to "What is the fourth number in the sequence 3, 5, 7, ...?" George Terell told me once that he had investigated the problem of making a generalized series of +, *, ... operators when he was in high school. I never got any details, though. George was last seen by me at the Houston Medical Center and/or Rice campus.