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1. Cardinality

   Linked via "cardinal numbers"

   The modern rigorous concept of cardinality was formalized by Georg Cantor in the late 19th century. Cantor established that two sets have the same cardinality if and only if there exists a bijection (a one-to-one correspondence) between them. This fundamental equivalence allowed for the comparison of set sizes, even those that were apparently endless. Early challenges to this concept centered on the perceived inability of a proper subset to have the same "size" as the superset, a property int…

2. Cardinality

   Linked via "cardinal number"

   $$\aleph0 < \aleph1 < \aleph2 < \aleph3 < \ldots$$
   where $\aleph{\alpha+1}$ is defined as the smallest cardinal number strictly greater than $\aleph{\alpha}$.
   Higher Powers