Definition:Rooted Tree/Ancestor Node
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Let $T$ be a rooted tree with root $r_T$.
Let $t$ be a node of $T$.
An ancestor node of $t$ is a node in the path from $t$ to $r_T$.
A proper ancestor node of $t$ is an ancestor node of $t$ that is not $t$ itself.
- Path in Tree is Unique: the path from $t$ to $r_T$ is indeed unique.
- Results about ancestor nodes can be found here.
- 1979: John E. Hopcroft and Jeffrey D. Ullman: Introduction to Automata Theory, Languages, and Computation ... (previous) ... (next): Chapter $1$: Preliminaries: $1.2$ Graphs and Trees: Trees
- 1996: H. Jerome Keisler and Joel Robbin: Mathematical Logic and Computability ... (previous) ... (next): $\S 1.7$: Tableaus