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=log(-1)(-1),…,here,we also ought to define that log(-1)(-1)=-1,so (-1)↑↑0=log(-1)[(-1)↑↑1] =log(-1)(-1)=-1≠1, (-1)↑↑(-1)=log(-1)[(-1)↑↑0] =log(-1)(-1)=-1≠0, (-1)↑↑(-2)=log(-1)[(-1)↑↑(-1)] =-1=log(-1)(-1)≠-∞. (-1)↑↑(-3)=log(-1)[(-1)↑↑(-2)] =-1=log(-1)(-1).

Tetration to real heights[edit]

The linear approximation method isn't easily a good approximation of tetration if the base is lower than 2. I am suprised there is no mention of any kind of Kneser's method being used for real- and complex-valued tetration. Using Kneser, the values should be: e^^(pi/2) ~ 5.82366 (against 5.868...) and 0.5^^-4.3 = log_0.5(log_0.5(log_0.5(log_0.5(0.5^^-0.3)))) ~ -1.07191 - 3.10267i (against 4.03335...). In the quadratic approximation, 2^^0.5 ~ 1.45933..., but Kneser yields 1.45878. Kwékwlos (talk) 12:28, 16 February 2023 (UTC)Reply[reply]

Usage in speech[edit]

What's the correct way to refer to the tetration operation when reading a mathematical expression out loud? For example, when reading the expression 3↑↑5, would you say, "three tetrated to five," or "three to the fifth tetration," or some such thing? — Preceding unsigned comment added by Mvrog (talkcontribs) 23:09, 27 April 2023 (UTC)Reply[reply]