Example of a bounded lattice that is NOT complete I know that every complete lattice is bounded. Is there a simple example for a bounded lattice that is not complete?
Thank you 

Update: My answer below is wrong! (Thanks to bof for pointing that out.) I will leave the answer here because I think my mistake and bof's comment could maybe be instructive.
Let $\mathbb{N}$ be the set of natural numbers. Let $\mathcal{P}_{fin}(\mathbb{N})$ denote the collection of finite subsets of $\mathbb{N}$. Then $L=\mathcal{P}_{fin}(\mathbb{N})\cup\{\mathbb{N}\}$ is a bounded lattice under inclusion. However, it is not complete since $\{0\}\cup\{2\}\cup\{4\}\cup\{6\}\cup\ldots$ is not in $L$.
