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  "body": "\n## Definition\n\nLet $F$ be an [[ordered field|0P3VCBDEE2]], let $V$ be a vector space over $F$, and let $P$ be an [[affine space|09XNAPTJQ7]] over $V$.\nLet $x, y, z \\in P$.\nThe point $y$ is *weakly between* $x$ and $z$ if $y = x + t(z - x)$ for some $t \\in F$ with $0 \\le t \\le 1$.\nThe point $y$ is *strictly between* $x$ and $z$ if it is weakly between them and $y \\ne x$ and $y \\ne z$.\n\n## Remarks\n\nExample: in $\\R^2$, the point $(1, 1)$ is strictly between $(0, 0)$ and $(2, 2)$, with $t = 1/2$.\nNon-example: $(3, 3)$ is on the line through $(0, 0)$ and $(2, 2)$, but it is not between them, since it needs $t = 3/2 \u003e 1$.\nWeak betweenness is symmetric: if $y$ is weakly between $x$ and $z$, then it is weakly between $z$ and $x$, with $1 - t$ in place of $t$.\nThe set of points weakly between $x$ and $z$ is the closed segment $[x, z]$.\nIn axiomatic geometry, betweenness is not defined but taken as a primitive relation that satisfies the axioms of order.\n",
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