Cardinality of the set of all partitions of N which contain only finite sets? My intuition tells me c would be the answer but don't know how to proof that.
2026-03-29 17:33:59.1774805639
cardinality of the set of all partitions of N which contain only finite sets
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Picking the minimum member of each partition set gives us an infinite subset of $\Bbb N$ and all infinite subsets of $\Bbb N$ can be made that way from some partition with finite sets.
The powerset of $\Bbb N$ has $\frak{c}$ member sets and only $\aleph_0$ of them are finite, so the set of infinite subsets of $\Bbb N$ also has size $\mathfrak{c}$..