Should tetration be a multivalued function?
#4
(01/03/2016, 11:24 PM)marraco Wrote: The problem is that the Z curve is not uniquely defined. It depends on the value choosen for \( \\[15pt]

{^0a} \). Any value between \( \\[20pt]

{{y_{\infty}} < ^0a < {y_{-\infty}}} \) is valid, and the only difference this choice make, is the horizontal displacement on the curve. I drew the Z curve matching the origin with his inflection point (roughly).

It appears that these 3 branches are not connected in the real line, but I would suspect that they are connected in the complex plane (to make a Riemann surface), and that fixing \( {}^0a = 1 \) on the main branch might fix the value of the other branches, at least that's what I would think.
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RE: Should tetration be a multivalued function? - by andydude - 01/04/2016, 12:01 AM

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