User blog comment:Alemagno12/Question/@comment-11227630-20180801021344

In "Hx(a,b)[n] = sup{Hn(a,b)|n<x}", the n is "free" in left side but "bound" in right side. Do you mean "Hx(a,b) = sup{Hn(a,b)|n<x}" or "Hx(a,b)[n] = Hn(a,b)"?