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  "body": "\n## Summary\n\nA normal function is a function from [[ordinals|0YSCSX5YZC]] to ordinals that is strictly increasing and continuous at limit ordinals.\nThe [[precise definition|PXTF18X433]] asks that the value at a limit be the supremum of the earlier values.\nEach normal function has arbitrarily large fixed points, and this fixed-point lemma is the engine behind the [[Veblen function|JQFAE9S2F4]] and many ordinal notations.\n\n## Explanations\n\n### L1 human\n\nA normal function climbs through the ordinals without jumps at limit points.\nAt a limit stage, its value is exactly the place that the earlier values were approaching.\nFor example, $\\alpha \\mapsto \\omega + \\alpha$ is normal: at $\\omega$ its value is $\\omega + \\omega$, the limit of $\\omega + 1, \\omega + 2, \\ldots$.\nThe function $\\alpha \\mapsto \\alpha + 1$ is not normal, because at $\\omega$ it jumps to $\\omega + 1$ while the earlier values approach only $\\omega$.\nBecause a normal function never skips a limit, it must eventually catch its own argument, and it has fixed points.\n",
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