User blog:Kel47/Exploding Tnotation part 2

Rules from previous blogpost: 1.Ta = 10^a, a \in Z+ The expression Ta means simply, 10 to the power of A. 2.aTb = 10^10^10^...10^b, where there are a 10s. 3.aTb@c = (c*a)Tb. 4.aTb@c...@y@z = aTb@c...@zTy 5.aTb@@c = aTb@c@c@c@c (c times) 6.aTb(@^c)d = aTb(@^c-1)d(@^c-1)d(@^c-1)d... (d times) 7.aTb(@^@)d = aTb(@^d)d (diagonalized)

To go further:

T1(@^@)2@3 = T1(@^@)3T2 = T1(@^3T2)3T2 This has a 10^10^10^2(googolplex) entries in the next line!

T1(@^@)10@@2 = T1(@^@)10@2@2 = T1(@^@)10@2T2 T1(@^@)(2T2)T10

Eventually, we can define aTb(@^@@)c as aTb(@^@)c(@^@)...c               c terms in expression aTb(@^@@@)c = aTb(@^@@)c(@^@@)...c

... Eventually, we reach things like aTb(@^@^5)c aTb(@^@^10)c aTb(@^@^@)c = aTb(@^@^c)c We can generalized this to tetration:

aTb(@^^@)c = aTb(@^^c)c = aTb(@^@^@...)c a power tower of @ that is c high