Show that, for any set , there is no surjection from to the power-set of .
Show that there exists an injection from to .
Let be a subset of . A section of is a subset of of the form
where and with . Prove that there does not exist a set such that every set is a section of .
Does there exist a set such that every countable set is a section of [There is no requirement that every section of should be countable.] Justify your answer.