Given a partially ordered set $(U,\leq )$, its maximum is always a maximal, but none of its maximals may necessarily be a maximum, right?
In which cases is none of the maximals a maximum?
I understand the concept and I know that they are not the same, what I don't see is in which cases the maximals are not maximum. It's very clear with the order relationship of $|$ (divide a), but I don't understand it very well with the canonical relationship of the naturals ($\leq $).