Climb into Cantor’s Attic, where you will find infinities large and small. We aim to provide a comprehensive resource of information about all notions of mathematical infinity.

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**Sources**

Cantor's Attic (original site)

Joel David Hamkins blog post about the Attic

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

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The *continuum hypothesis* is the assertion that the continuum is the
same as the first uncountable cardinal
$\aleph_1$.
The *generalized continuum hypothesis* is the assertion that for any
infinite cardinal $\kappa$, the power set $P(\kappa)$ has the same
cardinality as the
successor
cardinal $\kappa^+$. This is equivalent, by transfinite induction, to
the assertion that $\aleph_\alpha=\beth_\alpha$ for every ordinal
$\alpha$.