# Tetration with 0 < #s < 1?

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?

• 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 $\exp(1/e)$. – Oscar Lanzi Nov 13 '17 at 0:53
• wow thx .. and so beautifully unintuitive for #s > 1 .. O.O – SMicheal Nov 13 '17 at 1:03
• can u help with my irrational density question? – SMicheal Nov 13 '17 at 1:05
• Start at en.wikipedia.org/wiki/Tetration. – Oscar Lanzi Nov 13 '17 at 1:12