I am reading Apostol's Calculus. On page 74, section 1.17, it claims that every number in $S$ is less than every number in $T$. If I understand it correctly, that can only happen if $S$ doesn't have maximum element and $S$ doesn't have minimum element. The sets will have supremum and infimum. I'd like to confirm my understanding is correct.
Then, I'd would like to know which theorem tells us $S$ and $T$ cannot have maximum and minimum element respectively.
