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{{Short description|Theorem in order theory}}
{{otheruses4|Kleene's fixed-point theorem in lattice theory|the fixed-point theorem in computability theory|Kleene's recursion theorem}}
[[File:Kleene fixpoint svg.svg|thumb|Computation of the least fixpoint of ''f''(''x'') = {{sfrac|1|10}}''x''<sup>2</sup>+[[arctangent|atan]](''x'')+1 using Kleene's theorem in the real [[interval (mathematics)|interval]] [0,7] with the usual order]]
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