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  "body": "\n## Description\n\nThe cardinality of the continuum, written $\\mathfrak{c}$, is the [[cardinal number|0QKPNZKNEA]] $2^{\\aleph_0}$.\nIt is the cardinality of the [[power set|0BC7KX51Z8]] of $\\mathbb{N}$, and of the set of all sequences of $0$ and $1$.\nIt is also the cardinality of $\\mathbb{R}$. See [[the reals have the cardinality of the continuum|075PM9FH7A]].\n\n## Remarks\n\nBy [[Cantor's theorem|0WTEMGYV2C]], $\\mathfrak{c} \u003e \\aleph_0$.\nOther sets of cardinality $\\mathfrak{c}$ are each nonempty open interval of $\\mathbb{R}$, the plane $\\mathbb{R}^2$ and the set of irrational numbers.\nThe [[continuum hypothesis|0MN2MER9WN]] says that $\\mathfrak{c} = \\aleph_1$.\n\n## Explanations\n\n### L1 human\n\n$\\mathfrak{c}$ is the size of the real line.\nIt is a larger infinity than $\\aleph_0$.\nSurprisingly, a short interval, a whole line and a whole plane all have this same size.\n",
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