I'm going through Brewer's theorem and its proof by Nancy Lynch and Seth Gilbert. But the paper left me with one question. What prevents the theorem from being applicable to a single node?
I haven’t encountered any explicit definition of network partition that restricts its applicability to a network. There are some hints in  that suggest that a network partition with a single node would mean cutting off all communication to that node itself. This doesn’t make a whole lot of sense to me because you could always have a partition with all the service nodes on one side and the client node on the other. No service could possibly tolerate that.
A single node data object can be consistent and available if requests sent to it get through. To me, the definition of a network partition and where it applies leaves something to be desired. What am I missing here?
 Brewer’s Conjecture and the Feasibility of Consistent, Available, Partition-Tolerant Web Services by Seth Gilbert and Nancy Lynch