# Definition:Rooted Tree/Child Node

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## Definition

Let $T$ be a rooted tree with root $r_T$.

Let $t$ be a node of $T$.

The **child nodes** of $t$ are the elements of the set:

- $\left\{{s \in T: \pi \left({s}\right) = t}\right\}$

where $\pi \left({s}\right)$ denotes the parent mapping of $s$.

That is, the **children** of $t$ are all the nodes of $T$ of which $t$ is the parent.

### Grandchild Node

A child of a child node of a node $t$ can be referred to as a **grandchild node** of $t$.

In terms of the parent mapping $\pi$ of $T$, a **grandchild node** of $t$ is a node $s$ such that:

- $\pi \left({\pi \left({s}\right)}\right) = t$

## Also known as

**Child nodes** are often referred to as just **children**.

## Sources

- 1996: H. Jerome Keisler and Joel Robbin:
*Mathematical Logic and Computability*... (previous) ... (next): $\S 1.7$: Tableaus