Revision as of 05:48, 17 September 2024 edit RJFJR (talk \| contribs) Administrators 166,819 edits →Proof{{Cite book\|title=Mathematical Theory of Domains by V. Stoltenberg-Hansen\|last=Stoltenberg-Hansen\|first=V.\|last2=Lindstrom\|first2=I.\|last3=Griffor\|first3=E. R.\|publisher=Cambridge University Press\|year=1994\|isbn=0521383447\|pages=24\|language=en\|doi=10.1017/cbo9781139166386\|url=https://archive.org/details/mathematicaltheo0000stol/page/24}}: move ref out of heading ← Previous edit		Revision as of 14:23, 7 May 2025 edit undo 2a02:1812:110c:dc00:612f:7713:b978:b460 (talk) No edit summary Next edit →
Line 17: Although [[Tarski's fixed point theorem]] does not consider how fixed points can be computed by iterating ''f'' from some seed (also, it pertains to [[monotone function]]s on [[complete lattices]]), this result is often attributed to [[Alfred Tarski]] who proves it for additive functions.<ref>{{cite journal \| author=Alfred Tarski \| url=http://projecteuclid.org/Dienst/UI/1.0/Summarize/euclid.pjm/1103044538 \| title=A lattice-theoretical fixpoint theorem and its applications \| journal = [[Pacific Journal of Mathematics]] \| volume=5:2 \| year=1955 \| pages=285–309}}, page 305.</ref> Moreover, the Kleene ~~Fixed~~fixed-~~Point~~point ~~Theorem~~theorem can be extended to [[monotone function]]s using transfinite iterations.<ref>{{cite journal \| author=Patrick Cousot and Radhia Cousot \| url=https://projecteuclid.org/euclid.pjm/1102785059 \| title=Constructive versions of Tarski's fixed point theorems \| journal = Pacific Journal of Mathematics \| volume=82:1 \| year=1979 \| pages=43–57}}</ref> == Proof ==

Kleene fixed-point theorem: Difference between revisions