 Observe that finite subsets of a set \(X\) are exactly the finite elements of the complete lattice of subsets of \(X\). It is useful also to observe that this definition only partially matches our intuition: consider for example the finite element \(\infty + 1\) in the cpo   \[0 \sqsubseteq 1 \sqsubseteq 2 \sqsubseteq \cdots \sqsubseteq \infty \sqsubseteq \infty + 1.\]   