Hello agian
in the quizzes there is this true or false questions
Given $X$ and $Y$ two subsets of a ordered set such that $x<y$ for all $x\in X$ or $y\in Y$ then $\sup X<\inf Y$.
This is false. To be true we should allow for the possibility for $\sup X=\inf Y$
Example: in $\mathbb{R}$ with the usual order let $X=(0,1)$ and $Y=[1,2)$ then $\sup X=1=\inf Y$
I hope this helps :)