From: utzoo!utcsrgv!wessels Newsgroups: net.math Title: Re: x**x**x**x... : Where did I go wrong? Article-I.D.: utcsrgv.475 Posted: Sat Jul 17 21:09:48 1982 Received: Sat Jul 17 21:27:33 1982 References: mh3bs.178 The problem was to solve for x, where x**x**x**x... = 2 [x**x**x == x**(x**x)]. By observing that x**x**x**x... = x**(x**x**x...) = x**2 one might deduce that x=sqrt(2) is the(an) answer. In fact, my calculator seems to agree that the series x,x**x,x**x**x,... where x=sqrt(2) converges to a limit of 2. By a simple extension to the above argument, one might show that the solution to general problems of the form x**x**x... = n will be x=n**(1/n). However, in the case of n=4, we find that x=4**(1/4)=sqrt(2)!! I think I'm just going to go home and cry into my pillow ... Ron Wessels U. of Toronto ...!decvax!utzoo!utcsrgv!wessels