User blog comment:Vel!/Yudkowsky on googology/@comment-5982810-20140327230703/@comment-5029411-20140327232405

X{a}{b}...{y}{z}Y = X{a+b...y+z}Y

X{^}Y = X{X{^}Y-1}X

X{^}1 = X

X{^}{^}Y = X{^}{X{^}{^}Y-1}X

E100 #{^*#}# 100 = E100 #{^*100}# 100

X{^^}Y = X{^*X{^^}Y-1}Y

E100(X Y)100 = E100(X  Y)100

{X,Y,1,2} = X X/w Y nested