- #1
Kittel Knight
- 99
- 1
Consider the equation
[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?
[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?