I can't seem to figure out how to respond directly to a topic in the arithmetic/algebra column, so I'll say it here. I remeber being given this problem in the following form.
Solve: x^(x^(x^...) = 2 The elippsis indicate an infinite nesting of the exponents. A cute solution is to note that the exponent of the lowest x is the entire expression itself. i.e.
in x^ the square bracket encloses an expression which is the same as the original expression. So that the exponent on x is 2 or x^2 = 2 and x= sqrt(2). This is cute but to challenge the claim made in the page I read try this if you replace the right side with any value a, then the solution of x^(x^(x... = a would be x = a^(1/a). Now try this: a=4. Go ahead, try it.