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  "body": "\n## Summary\n\nBetweenness is the relation \"the point $y$ lies between the points $x$ and $z$\".\nIn an [[affine space|09XNAPTJQ7]] over an [[ordered field|0P3VCBDEE2]] it means that $y$ lies on the segment from $x$ to $z$.\nIn axiomatic geometry it is a primitive relation, and the axioms of order, such as [[Pasch's axiom|KJT98G16Y4]], describe it.\nSegments, rays, half-planes and the inside of a triangle are all defined from it.\n\n## Explanations\n\n### L1 human\n\nWalk along a straight road from $x$ to $z$.\nEvery point you pass on the way is between $x$ and $z$.\nOn the number line, $2$ is between $1$ and $5$, and $7$ is not.\nThis simple idea of order along a line is enough to define segments and sides of a line.\n",
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