I'm pretty interested into hyper operators, but they are only defined for integers :
$H_0(a,b)=b+1$ succession
$H_1(a,b)=a+b$ addition
$H_2(a,b)=ab$ multiplication
$H_3(a,b)=a^b$ exponentiation
...
I already proposed a extension to relative numbers using inverses of the functions ($H_{-1}(a,b)=a-b$ subtraction) But is there a way to define $H_{1.5}$? A operator between addition and multiplication, "addiplication". Or $H_{2.63}$, $H_{-0.21}$,etc... I heard about the Akerman function in this topic, but I don't really see how it is related
