The obligatory question on countability/uncountability.
5C. Define what is meant by the term countable. Show directly from your definition that if is countable, then so is any subset of .
Show that is countable. Hence or otherwise, show that a countable union of countable sets is countable. Show also that for any , is countable.
A function is periodic if there exists a positive integer such that, for every , . Show that the set of periodic functions is countable.