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From: stevev@tekchips.UUCP (Steve Vegdahl)
Newsgroups: net.puzzle
Subject: Re: x to the x to the x ... (ANSWER/SPOILER)
Message-ID: <481@tekchips.UUCP>
Date: Fri, 3-May-85 13:35:54 EDT
Article-I.D.: tekchips.481
Posted: Fri May  3 13:35:54 1985
Date-Received: Sun, 5-May-85 23:41:28 EDT
References: <7219@watdaisy.UUCP> <3681@alice.UUCP>
Organization: Tektronix, Beaverton OR
Lines: 24

> He is mistakenly assuming that exponentiation is left-associative,
> where it is really right-associative.

Mumble.  Left- or right-associativity is not a property of a function;
it is rather a is matter of notional convention.  The subtraction
operator ('-') is left-associative in Pascal, but right-associative in APL.
Traditionally in mathematics, exponentiation has been denoted by making
the exponent smaller (and higher and to the right ...), or possibly by a
notation such as exp(x,y).  (Both of these are more or less unambiguous).

My strong impression (correct my if I am mistaken) is that the '^' operator
has been used to denote exponentiation only since the advent of
programming languages, ascii terminals, etc.  While it may be true that
most programming languages that use '^' for exponentiation define it to be
right-associative, I do not find either interpretation to be unreasonable.

Ideally, it would have been nice if the original problem had been
parenthesized so as to be unambiguous.


		Steve Vegdahl
		Computer Research Lab.
		Tektronix, Inc.
		Beaverton, Oregon