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  "body": "\n## Definition\n\nThe binary trees are defined recursively by these two rules.\nThe empty tree is a binary tree. It has no nodes.\nIf $L$ and $R$ are binary trees, then $\\operatorname{node}(L, R)$ is a binary tree. It has one more node than $L$ and $R$ together, the root, with left subtree $L$ and right subtree $R$.\nEvery binary tree comes from these two rules in a unique way, in finitely many steps.\n\n## Remarks\n\nThe left and right subtrees are ordered. Thus $\\operatorname{node}(\\operatorname{node}(\\varnothing, \\varnothing), \\varnothing)$ and $\\operatorname{node}(\\varnothing, \\operatorname{node}(\\varnothing, \\varnothing))$ are different binary trees with $2$ nodes.\nThe number of binary trees with $n$ nodes is the Catalan number $C_n$. The node [[binary trees are counted by Catalan numbers|0Y97E2DMB7]] states this.\nA nonempty binary tree is a [[rooted tree|0C9J6W2A8A]] in which each vertex has at most two children, each marked left or right.\n\n## Explanations\n\n### L1 human\n\nA binary tree is either empty, or a root with a left part and a right part that are binary trees again.\nBinary trees are used in computer science to store data for fast search.\n",
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