10/23/2022, 09:09 PM
(10/18/2022, 12:56 AM)Daniel Wrote: OK, more stuff. I understand renormalization to be the process in physics based on moving up to the successor hyperoperator. [...]
While I have given thought to non-integer and complex hyperoperators, I have nothing to report. My difficulty is I have no expectation of what would be found in such systems, no tests to validate any possible solutions. I do think the integer hyperoperators including \[x\uparrow^\infty \infty\] would need to be understood, before complex hyperoperators because a complex hyperoperator expression would likely be created from the entire set of hyperoperators.
Thank you for you contribution Daniel. This is a very interesting view. I find the topic of renormalization completely beyond my understanding but overall I have a feeling that higher operations has something to do with some mathematical physics. Also your last line deserve to be considered as an option. It is an interesting analogy that JmsNxn explored: finding non-integer ranks as limit of infinite composition of integer ranks. If that was the case we would be in computational deep troubles....since that would mean practical inaccessibility of non-integer ranks.
Mother Law \(\sigma^+\circ 0=\sigma \circ \sigma^+ \)
\({\rm Grp}_{\rm pt} ({\rm RK}J,G)\cong \mathbb N{\rm Set}_{\rm pt} (J, \Sigma^G)\)