giles@ucf-cs.UUCP (Bruce Giles) (02/25/84)
.< kernel for the line eater This is a really dumb question, but I can't figure out where else to turn.... For complex numbers a, b, and c; is (a ^ b ^ c) equal to: (1): a ^ (b ^ c) (2): (a ^ b) ^ c, or (3): a ^ (b * c) ave discordia going bump in the night ... bruce giles decvax!ucf-cs!giles university of central florida giles.ucf-cs@Rand-Relay orlando, florida 32816
leimkuhl@uiuccsb.UUCP (02/28/84)
#R:ucf-cs:-119800:uiuccsb:9700025:000:214 uiuccsb!leimkuhl Feb 27 13:42:00 1984 The operator ^ is non-associative, so a^b^c has no meaning-- you must specify the order in which the operations are to be performed. Perhaps this answers your questions: a^(b^c) != (a^b)^c. Ben Leimkuhler
ljdickey@watmath.UUCP (Lee Dickey) (03/31/84)
> For complex numbers a, b, and c; is (a ^ b ^ c) equal to: > (1): a ^ (b ^ c) > (2): (a ^ b) ^ c, or > (3): a ^ (b * c) Your question is not dumb, it is a perfectly natural one. To give an explanation, I would like to talk about "+", another dyadic function. It is a well known property of integers, rationals, reals, complexes (and other things, for that matter) that (a+b)+c = a+(b+c) That is why the expression "a+b+c" makes any sense at all, because addition is *defined* for only two numbers at a time, not for three or more. Now, what about exponentiation? It, like addition, is defined for only two numbers at a time. Now, does the expression "a^b^c" make sense? Most professional mathematicians are a bit twitchie about it, simply because of the observation that you made that gave rise to the question, namely that expressions (1) and (2) are not equivalent. I guess I am saying that there is no consensus, and that the pros try to be un-ambiguous about it by putting in the parentheses. -- Lee Dickey, University of Waterloo. (ljdickey@watmath.UUCP) ...!allegra!watmath!ljdickey ...!ucbvax!decvax!watmath!ljdickey
gwyn@brl-vgr.ARPA (Doug Gwyn ) (04/03/84)
The tradition is to make exponentiation right-associative so that a ^ b ^ c is the same as a ^ ( b ^ c ). A little thought should make clear why left-associativity would not be as useful a convention.