Normal function

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Revision as of 20:48, 5 September 2022 by Metachirality (talk | contribs) (Created page with "A normal function is a function on ordinals that preserves limits and is strictly increasing. That is, \(f\) is normal if and only if it satisfies the following properties: * \(\alpha<\beta \Leftrightarrow f(\alpha)<f(\beta)\) * \(f(\alpha)=\sup f(\beta)\) if and only if \(\beta<\alpha\) and \(\alpha\) is a limit ordinal.")
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A normal function is a function on ordinals that preserves limits and is strictly increasing. That is, \(f\) is normal if and only if it satisfies the following properties:

  • \(\alpha<\beta \Leftrightarrow f(\alpha)<f(\beta)\)
  • \(f(\alpha)=\sup f(\beta)\) if and only if \(\beta<\alpha\) and \(\alpha\) is a limit ordinal.
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