Fixed point

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The fixed point of a function, LaTeX: f:X \rightarrow X, is an element LaTeX: x \in X such that LaTeX: f(x)=x. Of a point-to-set map, LaTeX: F:X \rightarrow 2^X, we instead have that LaTeX: x \in F(x). The study of fixed points has been at the foundation of algorithms. Moreover, forcing substructure.


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