User blog comment:Edwin Shade/A Three-Symbol System For Representing Ordinals/@comment-25601061-20171105181304

We don't need labels until we reach ωω ω. Let [] is a bigger pair of parentheses than.


 * [(]|[)] = ωω
 * ([(]|[)]) = ωω+1
 * [(][(]|[)][)] = ωω2
 * [(][(][(]|[)][)][)] = ωω3
 * ([(])|([)]) = ωω 2
 * (([(]))|(([(])) = ωω 3
 * [(]1[(][)]1|[(]1[(][)]1 = ωω ω