What does it mean for a linear order to be dense or without endpoint?

Question

So What does it mean for a linear order to be

• Dense
• Without EndPoint

Example (R, <), which one is this and why?

Answer 1

A linear order is dense when for all $x,y$ such that $x < y$ there is some $z$ with $x < z < y$. In $\mathbb{R}$ we can take $\frac{x+y}{2}$ e.g. So there are always points between any two distinct points.

Without endpoint means it has no minimum or maximum. So for all $x$ there is some $y$ with $y>x$ and some $z$ with $z < x$. In $\mathbb{R}$ we can always take $x+1$ or $x-1$ for that, e.g.