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