User blog comment:Googleaarex/Hyper-Operators Numbers/@comment-25371339-20140917182428/@comment-25371339-20140917184501

New expansion!

n<>x =  nn n n ... n   w/ x levels

n<>n<> x = n<>n n n n ... n     w/ x levels

We can also define n<<>>x as a nest of n<>x, n<<<<m>>>>x as a nest of n<<<m>>>x, etc.

The limit of this is n<<<...<<<m>>>...>>>x