# Definition:Binary Tree

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## Definition

A **binary tree** is a rooted tree which has at most two branches at any node.

That is, every node in a **binary tree** has (apart from the root) degree of either $1$ (for the leaf nodes) or $3$ (one for the parent, two for the children).

### Branches

The branches at any particular node of a binary tree are frequently called the **left-hand branch** and the **right-hand branch**, and a distinction is made between them.

## Applications

**Binary trees** are frequently used in computer science to store data in an efficiently searchable fashion.

## Sources

- 1998: David Nelson:
*The Penguin Dictionary of Mathematics*(2nd ed.) ... (previous) ... (next):**binary tree** - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next):**binary tree**

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- 2014: Christopher Clapham and James Nicholson:
*The Concise Oxford Dictionary of Mathematics*(5th ed.) ... (previous) ... (next):**binary tree**