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From: wws@whuxlm.UUCP (Stoll W William)
Newsgroups: net.puzzle
Subject: Re: x to the x ... : exponentiation not associative
Message-ID: <755@whuxlm.UUCP>
Date: Tue, 30-Apr-85 17:24:39 EDT
Article-I.D.: whuxlm.755
Posted: Tue Apr 30 17:24:39 1985
Date-Received: Wed, 1-May-85 04:11:15 EDT
References: <558@hou2e.UUCP>
Organization: AT&T Bell Laboratories, Whippany
Lines: 38

> Exponentiation is not associative.
> This solution depends on interpreting the problem definition as
> 
> 	x^(x^(x^(x^... = 2,
> 
> in which case x = sqrt(2) is the correct solution.
> 
> This solution has been shown to be incorrect by several posters
> who have interpreted the problem definition as
> 
> 	(((...((x^x)^x)^x)...)^x) = 2.
> 
> In this case x = sqrt(2) => L.H.S. = oo.
> If interpreted this way, the problem has no solution, since
> 	
> 	(((...((x^x)^x)^x)...)^x) = oo  for all x > 1.

x^(x^(x^(x^... = 2 is how the C compiler would interpret the
equation (if it didn't choke on all the x's  %-) )

> 
> Now I have a question.
> 
> 	x^(x^(x^(x^... = 2  implies  x = sqrt(2)  as shown earlier.
> 
> 	Then in the equation x^(x^(x^(x^... = 4, we can perform a similar
> 	substitution to obtain
> 
> 		x^4 = 4  =>  x = sqrt(2).
> 
> 	How can the L.H.S. using x = sqrt(2) equal both 2 and 4?
> 
> 				Jeff Heatwole
> 				..!hou2e!jlh

I'm stumped.  We should write to the Manufacturer.

Bill Stoll, ..!whuxlm!wws