proof of this:

x^x^x^.^.^. (infinite exponentiation) only converges for e^(-e)<x<e^(1/e)

Please halp, for it is beyond me :(.

This isn't true. x = 1.2, for instance, will certainly diverge under infinite exponentiation, but e^(-e) < 1.2 < e^(1/e). Further, x = (0.01)^(100) will converge to 0.01 under infinite exponentiation, but 0.01 < e^(-e).