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From: ljdickey@watmath.UUCP (Lee Dickey)
Newsgroups: net.math
Subject: Re: Dumb Question
Message-ID: <7422@watmath.UUCP>
Date: Sat, 31-Mar-84 11:06:26 EST
Article-I.D.: watmath.7422
Posted: Sat Mar 31 11:06:26 1984
Date-Received: Sun, 1-Apr-84 07:03:54 EST
References: <1198@ucf-cs.UUCP>
Organization: U of Waterloo, Ontario
Lines: 29

   > 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)
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