User blog comment:Rgetar/Ordinal Explorer Online/@comment-31040770-20200220105600/@comment-32213734-20200220213805

If β < c then [X]β < c for any X. So [X] < c for any X.
 * L = [[c]c] = [c2] < c
 * L2 = [[c]c][[c]c] = [c2][c2] = [c2]L < c
 * [L2] = [L + L] = [L + [c2]] = [L + [c + c]] > [L + [c + L2]]
 * LL = [[[c]cc]cc]c[[c]c] = [[[L]L]L]L = [[L2]L]L = [L2]L < c
 * [LL] = [L[c2]] = [L[c + c]] > [L[c + L L] ]

All right now?