Sheldon L
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 Feb 7 revised An obvious pattern to $i\uparrow\uparrow n$ that is eluding us all? added taylor series Feb 7 revised An obvious pattern to $i\uparrow\uparrow n$ that is eluding us all? added taylor series Feb 6 comment An obvious pattern to $i\uparrow\uparrow n$ that is eluding us all? Thanks Gottfried. You might want to look at how sexp(z-0.1*I) looks too. As $\Re(z)$ goes to $-\infty$, it goes to the repelling fixed point, yet as $\Re(z)$ goes to $+\infty$ is is still going to the attracting fixed point. This is the big difference between the Schroeder function solution, and the Kneser solution. Feb 6 revised An obvious pattern to $i\uparrow\uparrow n$ that is eluding us all? extension of Kneser's solution Feb 6 comment An obvious pattern to $i\uparrow\uparrow n$ that is eluding us all? @DanielGeisler I am not aware of any treatment of the Abel equation on a sickle (using both fixed points) in Carleson & Gamelin. While Kneser's method only works for real bases>$e^{1/e}$, this method uniquely extends it to complex bases, including complex bases where one of the fixed points is indifferent or attracting. Feb 6 revised An obvious pattern to $i\uparrow\uparrow n$ that is eluding us all? added 88 characters in body Feb 6 revised An obvious pattern to $i\uparrow\uparrow n$ that is eluding us all? added 27 characters in body Feb 6 revised An obvious pattern to $i\uparrow\uparrow n$ that is eluding us all? added 238 characters in body Feb 6 answered An obvious pattern to $i\uparrow\uparrow n$ that is eluding us all? Jan 24 comment Infinite tetration of $i$ you are missing the "i"; $W(-\frac{\pi i}{2})$ should work, but it is difficult to work with the lambert W function in the complex plane. I get $-W(-\frac{\pi i}{2})/\frac{\pi i}{2}\approx 0.4383+0.3606i$ Oct 4 awarded Yearling Jul 14 accepted order of infinite countable ordinal numbers Jul 14 comment order of infinite countable ordinal numbers Thanks for the proof; much to learn. Jul 14 revised order of infinite countable ordinal numbers added 3 characters in body Jul 13 revised order of infinite countable ordinal numbers edited title Jul 13 comment order of infinite countable ordinal numbers @AsafKaragila I tried rewriting to make my question clearer. Jul 13 revised order of infinite countable ordinal numbers added 69 characters in body Jul 13 revised order of infinite countable ordinal numbers added 60 characters in body; edited title Jul 13 comment order of infinite countable ordinal numbers @AsafKaragila They are definitely NOT all equal. My question was clearly talking about ordinal arithmetic and the relative sizes or ordinal numbers Jul 13 comment order of infinite countable ordinal numbers @AsafKaragila I wanted to know the order of the sizes