The real line $\langle\mathbb{R},\lt\rangle$ is (up to isomorphism) the unique nonempty, separable, complete, endless total order.

The real line $\langle\mathbb{R},\lt\rangle$ is (up to isomorphism) the unique nonempty, separable, complete, dense, endless total order.

(All conditions are needed: Without separable we have for example $[0,1]\times\Bbb R$ with lexicographic order, without complete we have $\Bbb Q$, without dense we have $\Bbb Z$, without endless we have $[0,1]$, all with standard order)