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1. Natural Numbers

   Linked via "Transfinite arithmetic"

   The cardinality| $\aleph0$ exhibits unique arithmetic properties. For any natural number $k$, the union of $k$ disjoint sets, each having cardinality| $\aleph0$, still results in a set of cardinality| $\aleph0$. Furthermore, the product of two countably infinite sets yields a set of cardinality| $\aleph0$. Specifically, $\aleph0 \times \aleph0 = \aleph_0$.
   A related, though less intuitive, concept is the Ordinality of Natural Numbers, denoted $\omega$. While [cardinality](/entries/ca…