User blog comment:KthulhuHimself/Ordinal Arithmetic Notation (OAN)/@comment-34422464-20191112192546/@comment-27014275-20191113104559

The reason my definition works this way is because having it do this lines up hyperoperator ordinals with some of the large ordinals often used (w^^w is epsilon_0, w^^^w is zeta_0, w^[w]w is phi(0,w), etc). I'm going to expand this system quite a bit, too, mind you.