User blog:Alejandro Magno/Stronger Extended Up-Arrow Notation

I decided to extend my notation so it would be stronger.

Up to (^^(^^^^)^^) operator
Operators up to (^^^^) are defined as it follows.

Then:

a^(^^(n)^^)^b = a^(^(^(^(...(^(^(^(n)^)^)^)...)^)^)^)^b with n levels

a^(^^(^(^^(n)^^)^)^^)^b = a^(^^(^(^(^(...(^(^(^(n)^)^)^)...)^)^)^)^^)^b with n levels

and the new operator...

a^(^^(^(^(^^(n)^^)^)^)^b = a^(^^(^(^^(^(^^(...(^(^^(^(^^(^(^^(n)^^)^)^^)^)^^)^)...)^^)^)^^)^)^^)^)^^)^b with n levels

-- UNDER CONSTRUCTION --