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  "body": "\n## Statement\n\nLet $X$ be a real random variable with [[cumulative distribution function|0MXMS3AE13]] $F_X$.\nThen $F_X$ is nondecreasing: if $x \\le y$, then $F_X(x) \\le F_X(y)$.\n\n## Remarks\n\nThe proof: $\\{X \\le x\\} \\subseteq \\{X \\le y\\}$, so the claim follows from the [[monotonicity of probability|0464Z0JP2E]].\nMore precisely, $F_X(y) - F_X(x) = P(x \u003c X \\le y) \\ge 0$.\nA nondecreasing function has at most countably many points of discontinuity. So $P(X = x) \u003e 0$ for at most countably many $x$.\n\n## Explanations\n\n### L1 human\n\nAs $x$ moves to the right, the event \"$X \\le x$\" contains more outcomes, so its probability cannot go down.\n",
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