Infinite linear order with endpoints which is non-dense

Question

In the process of answering questions about normal models, I had to prove the following: Any normal model of $\chi$ is a non-dense linear order with a least and greatest element. The next question then asks to show that $\chi$ has an infinite normal model using the compactness theorem. My question is: Could anyone give me an example of an infinite non-dense linear order with a least and greatest element? I don't see how it's possible...

Answer 1

Consider $\Bbb Z\cup\{\pm\infty\}$.

Or consider $\Bbb N+\Bbb N^*$, that is, put all the non-negative integers on the bottom, then the negative integers on the top, but don't reverse the order of the negative integers, so you get something like this: $$0,1,2,3,\ldots,n,\ldots,-n,\ldots,-3,-2,-1$$