Continuum

From Cantor's Attic
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The continuum is the cardinality of the reals $\mathbb{R}$, and is variously denoted $\frak{c}$, $2^{\aleph_0}$, $|\mathbb{R}|$, $\beth_1$, $2^\omega$.

Continuum hypothesis

The continuum hypothesis is the assertion that the continuum is the same as the first uncountable cardinal $\aleph_1$.

Please greatly expand this entry.