# Fixed point

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.