math - What is the definition for the height of a tree?

Question

I can't seem to find a definitive answer for this, I'm trying to do some elementary proofs on heaps but here's what's throwing me off a little bit:

Is an empty tree valid? If so, what is its height?
I would think this would be 0.

What is the height of a tree with a single node?
I would think this would be 1 but I have seen definitions where it is 0 (and if this is the case then I don't know how to account for an empty tree).

Answer 1

Height of a tree is the length of the path from root of that tree to its farthest node (i.e. leaf node farthest from the root).

A tree with only root node has height 0 and a tree with zero nodes would be considered as empty. An empty tree has height of -1. Please check this.

I hope this helps.