·
The
subset of a countable set is countable.
·
Any
set that contains an uncountable set is uncountable.
·
If
A is an uncountable set and B is a countable set, then A – B is
uncountable.
·
The
union of two countable sets is countable.
·
The
union of a countable number of countable sets is countable.
·
The
set of rational numbers is countable.
·
The
set of irrational numbers is uncountable.
·
The
set of real numbers is uncountable.
·
The
set of all bit strings is countable.
·
The
set of all computer programs in a particular programming language is countable.
·
The
set of all functions from the positive integers to the set
{0,1,2,3,4,5,6,7,8,9} is uncountable.
·
There
are functions that are not computable.