Normal function: Difference between revisions
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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
* \(\alpha<\beta \Leftrightarrow f(\alpha)<f(\beta)\)
* \(f(\alpha)=\sup f(\beta)\) if and only if \(\beta<\alpha\) and \(\alpha\) is a [[limit ordinal]].
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