User blog comment:LittlePeng9/ITTM galore/@comment-10429372-20140318165300/@comment-1605058-20140318170332

Definition of codes for ordinals by Hamkins is the following: for given ordinal \(\alpha\) let \(\triangleleft\) be operation such that \((\mathbb{N},\triangleleft)\simeq(\alpha,<)\). Then real codea ordinal \(\alpha\) if \(n\)-th bit is 1 iff \(n=\langle a,b\rangle\) and \(a\triangleleft b\). To put it simplier, number codes ordinal if it codes corresponding order, and it codes corresponding order by marking \(\langle a,b\)rangle\)-th bit only if \(a\) is smaller than \(b\) in that order.