08/11/2010, 07:03 PM
ok , i must say i did not mention my assumption that the ' theta wave ' ( kneser curve ) is "smooth looking".
the shape of the theta wave is important ...
i assumed for all tetration solutions not yet mapping R -> R , that the theta wave is coo apart from the numbers [0,1,b,b^b,...] and looking " gauss-like ".
with gauss-like i mean that it looks like the error function , one single max value in the middle , symmetric , no local minimum.
for such a shape simple methods may be usefull.
such as newton iterations. at least for numerical solutions. on the other hand we are not just looking for 'a' tetration , but 'the' tetration.
regards
tommy1729
the shape of the theta wave is important ...
i assumed for all tetration solutions not yet mapping R -> R , that the theta wave is coo apart from the numbers [0,1,b,b^b,...] and looking " gauss-like ".
with gauss-like i mean that it looks like the error function , one single max value in the middle , symmetric , no local minimum.
for such a shape simple methods may be usefull.
such as newton iterations. at least for numerical solutions. on the other hand we are not just looking for 'a' tetration , but 'the' tetration.
regards
tommy1729
