User blog comment:Nayuta Ito/generalization of arrow notation/@comment-10429372-20141025122001/@comment-1605058-20141025123914

Unfortunatelly, tetration doesn't have as nice properties like (a^^b)^^c=a^^(b*c) or a^^(b^c), because (2^^2)^^2=4^^2=256, while 2^^(2*2)=2^^4=65536.