Term for: There Exists a Rational between every two Rationals?

Question

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?

Since you tagged the question as foundations, you might want to google the terms dense linear order and dense linear order without endpoins. — Git Gud, Jun 09 '14 at 19:13

score 9 · Accepted Answer · edited Apr 13 '17 at 12:19

9

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.

edited Apr 13 '17 at 12:19

Community

answered Jun 09 '14 at 19:08

Git Gud

1 Answers1