I have defined the ordered tree like this but it was not accepted by teacher, what is the formal definition?

Question

that is what I have defined "An Ordered Tree is a form of a rooted tree with a specific order of its nodes. Started from the root element the smaller number is on the left side and the higher number on the right side. "

but the teacher told me "Again, use of ordered trees are mixed here with their simple definition. Do not mix it"

I want the mathematical definition of ordered tree which is cite-able in paper. how can I define it?

Answer 1

How about

An ordered tree is a rooted tree with a total order on the set of children for each node

or

An ordered tree is a rooted tree together with a partial order $\preceq$ on the set of vertices by which vertices with same parent are comparable.

?

Augmented by

If in an ordered tree nodes $u,v$ have common parent, we say $u$ is to the left of $v$ (and $v$ is to the right of $u$) if $u\prec v$.