Theorem
The set of rational numbers
is everywhere dense in the set of real numbers![]()
Proof
The closure of the set of rational numbers
is the set of real numbers![]()
The interior of
is
hence![]()
Hence the set
of rational numbers is everywhere dense in![]()
Theorem
The set of rational numbers
is everywhere dense in the set of real numbers![]()
Proof
The closure of the set of rational numbers
is the set of real numbers![]()
The interior of
is
hence![]()
Hence the set
of rational numbers is everywhere dense in![]()