Rank of a well-founded tree
= Rank of a well-founded tree
{title2=$r(t)=\sup\{r(t^\frown x)+1:t^\frown x\in T\}$}
The rank of a terminal node is zero; the rank of any node is the supremum of the successor ranks of its immediate extensions. The rank of the empty node gives one convention for tree height. Every countable well-founded tree has countable rank. Changing between empty-root rank and successive leaf-deletion order changes harmless endpoint conventions.