Fixed point (mathematics)

Fixed points in mathematics are not to be confused with other uses of "fixed point", or stationary points where f'(x) = 0.
A function with three fixed points

In mathematics, a fixed point (sometimes shortened to fixpoint), also known as an invariant point, is a value that does not change under a given transformation. Specifically, for functions, a fixed point is an element that is mapped to itself by the function. Any set of fixed points of a transformation is also an invariant set.