WEEK 8
M: Cantor Theorem, Schroeder-Bernstein Theorem, Cardinals.
1.66. Cantor Theorem.
1.67. Schroeder-Bernstein Theorem.
1.68. Cardinal.
W: Basic facts about cardinals.
Remark.
On splits into half open intervals [\alpha,\alpha') where \alpha is a cardinal.
1.69. Definition and Proposition.
Cn = the class of all cardinals. This is really a class.
1.70. Proposition. If A is a set of cardinals
then sup(A) is a cardinal.
1.71. Theorem. Cn is a proper
class.
1.72. Proposition. (a) Every element
of \omega is a cardinal. (b) \omega is a cardinal.
1.73. Definition. Finite, countable and
uncountable sets.
1.74. Definition. The function \alpeph.
\aleph_\alpha, \omega_\alpha.
F: Holiday.