Editing Fixed point (mathematics) (section)

=== Least fixed point ===
{{Main|Least fixed point}}

In [[order theory]], the [[least fixed point]] of a [[function (mathematics)|function]] from a [[partially ordered set]] (poset) to itself is the fixed point which is less than each other fixed point, according to the order of the poset. A function need not have a least fixed point, but if it does then the least fixed point is unique.

One way to express the [[Knaster–Tarski theorem]] is to say that a [[monotone function]] on a [[complete lattice]] has a [[least fixed point]] that coincides with its least prefixpoint (and similarly its greatest fixed point coincides with its greatest postfixpoint).<ref>Yde Venema (2008) [http://staff.science.uva.nl/~yde/teaching/ml/mu/mu2008.pdf Lectures on the Modal μ-calculus] {{webarchive|url=https://web.archive.org/web/20120321162526/http://staff.science.uva.nl/~yde/teaching/ml/mu/mu2008.pdf|date=March 21, 2012}}</ref>