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When I try numbers between 0 and 1 on my calculator app n-calc on my phone .. I get rapid convergence when the numbers are close to 1 .. And alternating but slow convergence when numbers are close to zero .. The convergence is not 1 nor 0 but an irrational number between 0 and 1 .. is there a special name for the irr# i^i^i...? If not, may I?

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    $\begingroup$ It is not slow convergence when the input is close to zero. You get to a point where the oscillations settle down to a constant altitude but do not die out anymore. Tetration converges when the argument is conclusively between $\exp(-e)$ and $\exp(1/e)$. $\endgroup$ – Oscar Lanzi Nov 13 '17 at 0:53
  • $\begingroup$ wow thx .. and so beautifully unintuitive for #s > 1 .. O.O $\endgroup$ – SMicheal Nov 13 '17 at 1:03
  • $\begingroup$ can u help with my irrational density question? $\endgroup$ – SMicheal Nov 13 '17 at 1:05
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    $\begingroup$ Start at en.wikipedia.org/wiki/Tetration. $\endgroup$ – Oscar Lanzi Nov 13 '17 at 1:12

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