05/25/2014, 09:35 AM
Interesting thing. for integers ranks \( r=0 \) and \( r=1 \) the limit
\( lim_{K\rightarrow 1^+}\odot_{r}^K \)
is still addition and multiplication, but between I don't know (but I doubt... I'd except some dequantization phenomenon like for the tropical operations max and min)...
If someone has an extension for tetration to the reals he could check if for that extension the operations \( \odot_{r \in ]0,1[}^K \) satisfie you conjecture.
Probably JmsNxn knows more about it.
\( lim_{K\rightarrow 1^+}\odot_{r}^K \)
is still addition and multiplication, but between I don't know (but I doubt... I'd except some dequantization phenomenon like for the tropical operations max and min)...
If someone has an extension for tetration to the reals he could check if for that extension the operations \( \odot_{r \in ]0,1[}^K \) satisfie you conjecture.
Probably JmsNxn knows more about it.
Mother Law \(\sigma^+\circ 0=\sigma \circ \sigma^+ \)
\({\rm Grp}_{\rm pt} ({\rm RK}J,G)\cong \mathbb N{\rm Set}_{\rm pt} (J, \Sigma^G)\)