# Binary trees

## Assume:

- let T = nonempty binary tree
- let n = number of nodes
- let n_e = number of external nodes
- let n_i = number of internal nodes
- let h = height of T

## Then, T has following properties:

- height of the nonempty binary tree + 1
**is less than or equal to**the number of nodes in the binary tree**is less than or equal to**2^(height of the nonempty binary tree + 1) — 1 - 1
**is less than or equal to**number of external nodes in the nonempty binary tree**is less than or equal to**2^(height of the nonempty binary tree) - height of the nonempty binary tree
**is less than or equal to**number of internal nodes of the nonempty binary tree**is less than or equal to**2^(height of nonempty binary tree) — 1 - log of (number of nodes in nonempty binary tree) — 1
**is less than or equal to**height of the nonempty binary tree**is less than or equal to**number of nodes in nonempty binary tree — 1

… sorry this was one was also not finished :’-(

for context plan was to illustrate this using 3djs

See you next time