EDB — 08K

Exercises

1. [08K] Prerequisites:[073]↺↻.The type of well ordering of \(ℕ\) is called \(𝜔\). Given \(k≥ 2\) natural, \(ℕ^ k\) endowed with the lexicographical order is a well-ordered set (for [073]↺↻), and the type of ordering is called  \(𝜔^ k\). Show that \(𝜔^ k⪯𝜔^ h \) for \(h{\gt}k\), and that \(𝜔^ k,𝜔^ h \) do not have the same type of order.