05/09/2022, 11:19 PM
Again, idk If I'm gettng your point... I do not think generalized iteration is good for the section I have in mind, I don't think I have proposed it.
For me, generalized iteration is about widening the field of application of real complex dynamics of functions beyond the realm of real/complex times. I'd say also omega notation and iteration integral is part of that. Instead ranks are not directly about iterations, more like "iteration of recursive constructions", a kind of meta-iteration height: and all the hyperoperations and related studies have their focus on isolating and iterating these recursive constructions.
My proposal is this
I'm not sure to agree when you say
I do not think tetration falls under this. Probably Hyperoperations fall under what we could call "iteration of iteration" and variants of.. So maybe... meta-iteration theory? But to be honest I'd like to avoid technical terms to name subsection.
For me, generalized iteration is about widening the field of application of real complex dynamics of functions beyond the realm of real/complex times. I'd say also omega notation and iteration integral is part of that. Instead ranks are not directly about iterations, more like "iteration of recursive constructions", a kind of meta-iteration height: and all the hyperoperations and related studies have their focus on isolating and iterating these recursive constructions.
My proposal is this
Quote:Hyperoperations and related studies
"Discuss (the mathematics of) hyperoperations families, how to extend and generalize them."
I'm not sure to agree when you say
Quote:As Tetration would fall under a subset of all the topics Mphlee described for the new subsection.
I do not think tetration falls under this. Probably Hyperoperations fall under what we could call "iteration of iteration" and variants of.. So maybe... meta-iteration theory? But to be honest I'd like to avoid technical terms to name subsection.
Mother Law \(\sigma^+\circ 0=\sigma \circ \sigma^+ \)
\({\rm Grp}_{\rm pt} ({\rm RK}J,G)\cong \mathbb N{\rm Set}_{\rm pt} (J, \Sigma^G)\)
