WEEK 6  
M: Cantor normal form 
      1.54. Theorem. Cantor normal form.
W: Completion of ordinal arithmetic. Goodstein sequences.
      1.55. Proposition.  If  \varepsilon_n-k> \varepsilon'_m-k
                                       or  (\varepsilon_n-k= \varepsilon'_m-k     and \alpha_n-k > \alpha'_m-k) where 
                                       k is the least such (\varepsilon_n-k,\alpha_n-k) (\varepsilon'_m-k,\alpha'_m-k) then
                                       the ordinal with normal form determined by \varepsilon_i and \alpha_i  is strictily larger
                                       than the ordinal with normal form determinaed by   \varepsilon'_i and \alpha'_i    
      1.56. Entertainment. Goodstein sequences.
      1.57. Definition. Goodstein sequences.
      1.58. Theorem. (Goodstein) Goodstein theorem.
F:  Proof of Goodsetin theorem.