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.

View the Project on GitHub neugierde/cantors-attic

Quick navigation
The upper attic
The middle attic
The lower attic
The parlour
The playroom
The library
The cellar

Cantor's Attic (original site)
Joel David Hamkins blog post about the Attic
Latest working snapshot at the wayback machine


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

    This article is a stub. Please help us to improve Cantor's Attic by adding information.

Continuum hypothesis

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 $\alpha$.