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  2. The empty set has exactly one partition, namely. (Note: this is the partition, not a member of the partition.) For any non-empty set X, P = { X } is a partition of X, called the trivial partition.
    en.wikipedia.org/wiki/Partition_of_a_set
    Yes, the empty set does have a partition. Let's see what a partition is: given a set X X, a partition of X X is a set P P of nonempty subsets of X X such that each element of X X is contained in exactly one element of P P. Consider P = ∅ P = ∅.
    math.stackexchange.com/questions/2193873/is-wi…
    Yes, it's true that the emptyset as no non-empty subsets. Curiously this does not imply that there is no partition of ∅ ∅. ∅ ∅ is a partition of ∅ ∅. Note that every element of ∅ ∅ is a non-empty subset of ∅ ∅, vacuously. The (non-existent) elements are pairwise disjoint and have union equal to ∅ ∅, qed.
    math.stackexchange.com/questions/4384486/is-a-…
     
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