Given a complete metric space X and a function f: X->X with a Lipschitz constant of r on (0,1) (i.e contracting function) show that there is a unique point f(x) = x

Use a sequence with arbitrary x0 and xn=f(xn-1)

to get x as limit of the sequence.

How do I get the limit and how do i use this in proving that f(x)=x?