- #1

- 99

- 1

[tex]x^{x^{x^{...}}} = 2 [/tex]

Does x exist ?

Well, at first, I would say x=sqrt(2) , but is this ok?

In general, x^x^x^... = Z would imply x = Z^(1/Z)

But, if x>1, then x^x^x^... is crescent.

In other words, when "Z" increases, then "x" increases.

However, lim oo Z^(1/Z) = 1

So, if x^x^x^... increases, it means that "x" goes to 1 ?!

Where is the mistake?