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  "body": "\n## Statement\n\nLet $(X, d)$ be a [[metric space|063W5JMY85]].\nFor all points $x, y, z \\in X$,\n$$d(x, z) \\le d(x, y) + d(y, z).$$\n\n## Remarks\n\nThis is one of the four axioms of a metric.\nFor $X = \\mathbb{R}$ with $d(x, y) = |x - y|$, it is the [[triangle inequality|03HF5PMY5T]] for real numbers, with $a = x - y$ and $b = y - z$.\nA consequence is the reverse form $|d(x, y) - d(x, z)| \\le d(y, z)$ for all $x, y, z \\in X$.\n\n## Explanations\n\n### L1 human\n\nA direct path from $x$ to $z$ is never longer than a path that goes through a third point $y$.\nIn the plane, this says that one side of a triangle is at most the sum of the other two sides.\n",
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