Can a lattice be bounded and NOT Complete?

Question

Can a lattice be bounded and not complete and if yes can you please show an example?

Answer 1

Consider $\mathbb{Q} \cup \{\pm \infty\}$, which is a total order and hence a bounded lattice. However, there is no supremum of $\{x \in \mathbb{Q} \mid x^2 < 2\}$.