06/10/2022, 11:04 AM
Excuse me, I mean that I'm not sure anymore that those approximations are useful for the purpose of my research.
I'm, and I was, researching about a far reaching generalization of hyperoperations. I don't know your background so I'll make it self-contained. I'm studying special functions of the kind \({\bf g}:J\to X\) and maps of kind \(\rho:X\to \mathbb N \) for \(J\) a dynamical system. That means that fixing a \(\rho\) of that kind we can send each \(\bf g\) to a map \(\rho{\bf g}:J\to \mathbb N\). Here in this post, 8 years ago, I was initiating the study, with scarce success, of functions \(f:J\to \mathbb N\) that are of the form \(f=\rho{\bf g}\).
I'm, and I was, researching about a far reaching generalization of hyperoperations. I don't know your background so I'll make it self-contained. I'm studying special functions of the kind \({\bf g}:J\to X\) and maps of kind \(\rho:X\to \mathbb N \) for \(J\) a dynamical system. That means that fixing a \(\rho\) of that kind we can send each \(\bf g\) to a map \(\rho{\bf g}:J\to \mathbb N\). Here in this post, 8 years ago, I was initiating the study, with scarce success, of functions \(f:J\to \mathbb N\) that are of the form \(f=\rho{\bf g}\).
Mother Law \(\sigma^+\circ 0=\sigma \circ \sigma^+ \)
\({\rm Grp}_{\rm pt} ({\rm RK}J,G)\cong \mathbb N{\rm Set}_{\rm pt} (J, \Sigma^G)\)