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  "body": "\n## Summary\n\nThe beth numbers $\\beth_\\alpha$ are the infinite [[cardinal numbers|0EBACQFAZW]] obtained from $\\aleph_0$ by taking power sets again and again, and suprema at limit stages.\nSo $\\beth_0 = \\aleph_0$, and $\\beth_1 = 2^{\\aleph_0}$ is the cardinality of the real numbers.\nThe [[precise definition|ZC4BHVHWE9]] is by transfinite recursion.\nThe generalized continuum hypothesis says exactly that $\\beth_\\alpha = \\aleph_\\alpha$ for every ordinal $\\alpha$.\n\n## Explanations\n\n### L1 human\n\nStart with the size of the natural numbers.\nThe set of all subsets of the natural numbers is strictly bigger, by [[Cantor's theorem|0WTEMGYV2C]]; its size is $\\beth_1$, the size of the real line.\nThe set of all subsets of the real line is bigger still; its size is $\\beth_2$, the number of all functions from $\\R$ to $\\R$.\nThe beth numbers continue this ladder of power sets forever.\n",
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