Convergence of the sequence z, z^z , z^z^z, ... corresponds to spiraling inward to the point of convergence in the complex planepic.twitter.com/1eJOKrmjfn
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Oh darn :(
just consider the special case where z is real, then clearly you can see that 10^10^10, for example wont converge
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Yes but a counterexample for that could be a real number k, where k is less than or equal to one but greater than zero. I would imagine that if k is negative then the tetration would diverge, but given a number such as for example .5, that the tetration converges.
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just showing that it converges for small k isn't a counter example but yes there is a region of convergence .. but it's quite small it's [e^(-e), e^(1/e)]
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