TITLE: Term for: There Exists a Rational between every two Rationals?
QUESTION [7 upvotes]: The integers and the rationals have the same cardinality, but the rationals satisfy the property that:
$$
\forall p,q\in\mathbb{Q},\quad \exists r\in\mathbb{Q}\quad \textrm{s.t.}\quad p<r<q,
$$
while the integers don't. 
Is there a term for this property?

REPLY [9 votes]: Such an order on a set is called a dense order.
The notion of dense in topology is closely related to the one in order theory. See this answer.