Rank-Wise Approximations of Hyper-Operations

[Catullus]

JmsNxn
Yes, I agree with you, except I believe there are at least \( \aleph_1 \) solutions, the countable infinity of period 1 fixed points, the uncountable infinity of n-period fixed points like the period 2 fixed point of \( 0^0=1, 0^1=0 \). Then there are the countable infinite rationally neutral fixed points on the Shell Thron boundary.

Why would n period points, for n ∈ \mathbb{N}? How would you use the limit formula on them?

Please restate your question. Thanks.

How would you use periodic points to do continuous iterations of exponentials?
The limit formula uses fixed points usually, if not always.

Consider a period 3 fixed point of \( f^n(z) \). But to \( f^{3n}(z) \) the period 3 fixed points just become 3 fixed points.

Happy 100th post!