What is an Unjoinable Set?

A set is said to be unjoinable if it cannot be partitioned into two sets such that every element in one set has a corresponding element in the other set. In other words, there does not exist a partition of the set into two subsets such that every element in one subset has a matching element in the other subset.

For example, the set of all integers is unjoinable because there is no way to partition it into two subsets where every integer in one subset has a matching integer in the other subset. This is because the integers are not paired up with each other in any way, so there is no way to establish a correspondence between them.

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