User blog comment:Alejandro Magno/Make an extension of the Notation! (my style)/@comment-5982810-20140924233634/@comment-25371339-20140924235937

Extension 4:

(0[1]1)#n = (0,0,0,...,0,0,1)#n with n entries

(1[1]1)#n = (0[1]1)(0[1]1)(0[1]1)...(0[1]1)(0[1]1)(0[1]1)#n with n (0[1]1)'s

((0)[1]1)#n = (n[1]1)#n

(0,1[1]1)#n = ((((...(((n)))...)))[1]1)#n with n levels

etc.

Then:

(0[1]2)#n = (0,0,0,...,0,0,1[1]1)#n with n entries

(0[1](1))#n = (0[1]n)#n

(0[1]0,1)#n = (0[1](((...(((n)))...))))#n with n levels

etc.

Then:

(0[1]0[1]1)#n = (0[1]0,0,0,...,0,0,1)#n with n entries

(0[1]0[1]0[1]1)#n = (0[1]0[1]0,0,0,...,0,0,1)#n with n entries

etc.

Limit is (0[1]0[1]0[1]...0[1]0[1]0[1]1)#n