Surjective map on compact metric space Is there a surjective map $f:X\to X$ on compact metric spcace $(X, d)$ with the following condition?
There is $0<L<1$ such that $d(f(x), f(y))<Ld(x, y)$  for all $x,y\in X$

Hints:
Since $f(X)$ is compact, there exists $x,y\in X$ such that $d(f(x), f(y))$ is the diameter of $f(X)$. Then, what can you say about the diameter of $X$ using
$$ d(f(x), f(y)) \le Ld(x,y) ? $$
