Fixed point: Difference between revisions
no edit summary
OfficialURL (talk | contribs) (create stub) |
RhubarbJayde (talk | contribs) No edit summary |
||
Line 1:
In general mathematics, a '''fixed point''' of a function \(f:X\to X\) is any \(x\in X\) such that \(f(x)=x\). If \(f\) is a [[Normal function|normal]] [[ordinal function]], then the fixed points of \(f\) are precisely the closure points of \(f\): that is, for all \(\alpha\), we have \(f(\alpha) = \alpha\) iff, for all \(\beta < \alpha\), \(f(\beta) < \alpha\). Fixed points are useful in the definition and analysis of apeirological notations such as the [[Veblen hierarchy]] or [[Ordinal collapsing function|OCFs]].
|