0.1 Dense Order
In mathematics, a partial order or total order \(<\) on a set \(X\) is said to be dense if, for all \(x\) and \(y\) in \(X\) for which \(x<y\), there is a \(z\) in \(X\) such that \(x<z<y\).
That is, for any two elements, one less than the other, there is another element between them.
Some examples of sets with dense order include: - The rational numbers \(\mathbb{Q}\) - The real numbers \(\mathbb{R}\)