I don't believe all the comments pointing out that x^(x^...) converges only in a certain range are the best way to understand what's going on here. The way I se

I don't believe all the comments pointing out that x^(x^...) converges only in a certain range are the best way to understand what's going on here. The way I see it, the "solve for x" puzzle really just serves to obscure the true reasoning used: if y=sqrt(2)^y and z=sqrt(2)^z, then y=z. When put like this, we can see that this is clearly false: solutions to the equation need not be equal any more than all zeros of a polynomial need be equal.