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  "body": "\n## Statement\n\nLet $T$ be a finite [[tree|0MJ0JS72DZ]] with $n$ vertices.\nThen $T$ has exactly $n - 1$ edges.\n\n## Remarks\n\nA tree has at least one vertex, because it is connected. Thus $n \\ge 1$.\nProof by induction on $n$: for $n \\ge 2$ delete a leaf, which exists by the [[leaf lemma|0H8Q4MANBD]]. The rest is a tree with $n - 1$ vertices.\nA consequence: the sum of the degrees in a tree is $2n - 2$.\n\n## Explanations\n\n### L1 human\n\nBuild a tree by adding one vertex at a time, each joined to the tree by one new edge.\nYou start with $1$ vertex and $0$ edges, so at the end there is always one edge fewer than vertices.\n",
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