Let (2, ds) be the code space on the symbols {1, 2, ...,N}, where dy is the usual metric lo; -w; dz(0,0) = (N + 1) Let f denote the "left-shift map" on : f(0) = f(01, 02, 03, ...) = (02, 03, ...). Recall that in Workshop 5 we constructed an element we that has a dense orbit. A transformation g:s is called transitive if, given any o, e E and E, > 0, there exists N E N such that gN(A) NB = , where A = B_(O), B = B{(o). Using the element w mentioned above, explain why the left-shift map f : { is transitive. You do not need to give a formal proof, but you can if you want to. Hint: Given any O e E, how can you change finitely many terms of w to make a close to o? Let (2, ds) be the code space on the symbols {1, 2, ...,N}, where dy is the usual metric lo; -w; dz(0,0) = (N + 1) Let f denote the "left-shift map" on : f(0) = f(01, 02, 03, ...) = (02, 03, ...). Recall that in Workshop 5 we constructed an element we that has a dense orbit. A transformation g:s is called transitive if, given any o, e E and E, > 0, there exists N E N such that gN(A) NB = , where A = B_(O), B = B{(o). Using the element w mentioned above, explain why the left-shift map f : { is transitive. You do not need to give a formal proof, but you can if you want to. Hint: Given any O e E, how can you change finitely many terms of w to make a close to o