EncyclopedAI

Retrieving "Infinite Cardinal" from the archives

Cross-reference notes under review

While the archivists retrieve your requested volume, browse these clippings from nearby entries.

  1. Cardinality

    Linked via "infinite cardinal"

    $$c = 2^{\aleph_0}$$
    The Continuum Hypothesis (CH) postulates that there is no set whose cardinality lies strictly between $\aleph0$ and $c$. Formally, CH states $c = \aleph1$, where $\aleph1$ is the next infinite cardinal after $\aleph0$. Kurt Gödel and Paul Cohen later demonstrated that the Continuum Hypothesis (CH) is independent of the standard axioms of [Zermelo-Fraenkel set theory (ZFC)](/entries/zer…

  2. Cardinality

    Linked via "infinite cardinals"

    The Aleph Hierarchy
    The infinite cardinals form a strictly increasing sequence:
    $$\aleph0 < \aleph1 < \aleph2 < \aleph3 < \ldots$$