From complex to real tetration Daniel Long Time Fellow Posts: 281 Threads: 95 Joined: Aug 2007 10/16/2022, 08:07 AM (This post was last modified: 10/17/2022, 06:41 AM by Daniel.) Edit: Background I have finished the first version of my Flow Mathematica function which I have submitted to Wolfram for review. I decompose the problem of tetration and the Ackermann function into that of fractional iteration that my Flow function handles and the classical Ackermann function. Having the flow function gets me 90% of anywhere I want to go working with tetration.  The following is supposed to be a graph of tetration of e. Hopefully it is a broken implementation of tetration. The problem is the flow that crosses itself. Being homoclinic is a real problem for defining unique tetration. I wonder if anyone else has ever considered issue of being homoclinic. $^xe$ So instead of dealing with $^y x$ I can choose to use $^y (1+x)$. This is nice because it has a fixed point at x=0 giving $^y 1$. This fixed point is also on the real line resulting in a real domain and range. Daniel bo198214 Administrator Posts: 1,630 Threads: 106 Joined: Aug 2007 10/17/2022, 07:46 AM (This post was last modified: 10/17/2022, 07:48 AM by bo198214.) I am still not exactly sure what the shown curve is. I guess it is the image of the function $^xe$ of some interval (a,b). If this is right, which interval is shown? Also I would assume that the points $^1e=e$, $^0e=1$ or $^{-1}e=0$  are to be seen somewhere, but I don't see them. bo198214 Administrator Posts: 1,630 Threads: 106 Joined: Aug 2007 10/21/2022, 07:48 PM (10/17/2022, 07:46 AM)bo198214 Wrote: I am still not exactly sure what the shown curve is. I guess it is the image of the function $^xe$ of some interval (a,b). If this is right, which interval is shown? Also I would assume that the points $^1e=e$, $^0e=1$ or $^{-1}e=0$  are to be seen somewhere, but I don't see them. Daniel, any clarification? Daniel Long Time Fellow Posts: 281 Threads: 95 Joined: Aug 2007 10/21/2022, 07:55 PM (10/21/2022, 07:48 PM)bo198214 Wrote: (10/17/2022, 07:46 AM)bo198214 Wrote: I am still not exactly sure what the shown curve is. I guess it is the image of the function $^xe$ of some interval (a,b). If this is right, which interval is shown? Also I would assume that the points $^1e=e$, $^0e=1$ or $^{-1}e=0$  are to be seen somewhere, but I don't see them. Daniel, any clarification? The graph is pure bullshit because it is divergent. I took a bit to realize how broken it was. The range is from x=-20 to x=10. Just like logs, I'm having more success with $^y (1+x)$. Daniel « Next Oldest | Next Newest »

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