Tetration with 0 < #s < 1?

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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?