Definition:Fixed Point

Definition

Let $f: S \to T$ be a mapping.

Then a fixed point (or fixed element) of $S$ under $f$ is an $x \in S$ such that $\map f x = x$.

Also defined as

The concept of a fixed point is usually encountered in the context of self-maps, that is, where $S = T$.

Also see

• Definition:Fixed Element under Permutation

• Results about fixed points can be found here.

Sources

• 2010: Raymond M. Smullyan and Melvin Fitting: Set Theory and the Continuum Problem (revised ed.) ... (previous) ... (next): Chapter $3$: The Natural Numbers: $\S 4$ A double induction principle and its applications: Definition $4.13$