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  1. Cardinality

    Linked via "cardinality of the continuum"

    Sets whose cardinality is strictly greater than $\aleph0$ are called uncountable. The most famous example is the set of real numbers, $\mathbb{R}$. Cantor's diagonalization argument definitively proved that $|\mathbb{R}| > \aleph0$.
    The cardinality of the continuum, denoted by $c$, is defined as $|\mathbb{R}|$.
    $$c = 2^{\aleph_0}$$

  2. Cardinality

    Linked via "continuum"

    Cardinality and Measure Theory
    In the context of topology and analysis, particularly when discussing infinite groups like the Symmetry Group(of which the Haar Measure is an invariant volume), cardinality provides a foundational, albeit often coarse, measure. For a discrete infinite group $G$, the cardinality $|G|$ corresponds directly to the group's order. However, for [continuous groups](/…