Definition:Linear Continuum

Definition
A totally ordered set $\left({S, \preceq}\right)$ is said to be a linear continuum iff:
 * $\left({1}\right): \quad$ $\left({S, \preceq}\right)$ is densely ordered.
 * $\left({2}\right): \quad$ $\left({S, \preceq}\right)$ is Dedekind complete.