Page "Tree traversal" Paragraph 51

This can be alternatively interpreted as mapping the infinite depth binary tree onto this tree and then applying breadth-first traversal: replace the " down " edges connecting a parent node to its second and later children with " right " edges from the 1st child to the 2nd child, 2nd child to third child, etc.

Thus at each step one can either go down ( append a (, 1 ) to the end ) or go right ( add 1 to the last number ) ( except the root, which is extra and can only go down ), which shows the correspondence between the infinite binary tree and the above numbering ; the sum of the entries ( minus 1 ) corresponds to the distance from the root, which agrees with the 2 < sup > n − 1 </ sup > nodes at depth n − 1 in the infinite binary tree ( 2 corresponds to binary ).