Let

*f*:

**A**->

**A** be a

function.

*x* is called a

*fixed point* of

*f* if

*f(x)=x*.

Of course this means that no matter how many times we apply *f* to *x*, it remains the same. So we would expect *x* to be a limit for a process of repeatedly applying *f* to *any* point. Under certain conditions, a fixed point exists and satisfies this limiting property.