08/01/2021, 11:23 AM
Complement: Another example of multivalued iteration
We consider now the second iterative root of the function \( f(z)=z+\frac{1}{z} \)
And we can observe that the symmetry law \( fg=f\to{f^tg=f} \) applies to all of \( f(z),f^{1/2}(z),\frac{1}{f(z)},\frac{1}{f^{1/2}(z)} \)
Some of these statements that involving set theory are still hypothetical, remaining to be proved
(especially the A(z) part)
We consider now the second iterative root of the function \( f(z)=z+\frac{1}{z} \)
And we can observe that the symmetry law \( fg=f\to{f^tg=f} \) applies to all of \( f(z),f^{1/2}(z),\frac{1}{f(z)},\frac{1}{f^{1/2}(z)} \)
Some of these statements that involving set theory are still hypothetical, remaining to be proved
(especially the A(z) part)