1. Using symbolic dynamics, describe the itineraries of all points that eventually land on 0. How many such points are there?
2. Which points in I have orbits that eventually land on 0?
3. Give an example of a different point whose orbit fills the set X densely.
4. Give an example of a sequence whose orbit under the shift map comes arbitrarily close to the sequence (0, 0, 0, ...) but never lands on this sequence.