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  "body": "\n## Summary\n\nCardinal characteristics of the continuum are cardinals of a special kind.\nEach is the least size of a family of reals, or of sets of reals, with some combinatorial property.\nEach of them lies between $\\aleph_1$ and $\\mathfrak{c} = 2^{\\aleph_0}$, the [[cardinality of the continuum|0WC28W9DNM]].\nUnder the [[continuum hypothesis|0MN2MER9WN]] they all equal $\\aleph_1$, but without it they can take different values.\nThe provable inequalities between them form a rich theory.\nStandard examples, such as the bounding and dominating numbers, are [[defined|R8S00S3Z94]] separately.\n\n## Explanations\n\n### L1 human\n\nHow many meagre sets do you need to cover the real line?\nCountably many are never enough, by the Baire category theorem, and continuum many points, each one a meagre set, are always enough.\nSo the answer is some cardinal between $\\aleph_1$ and $2^{\\aleph_0}$.\nQuestions of this type define the cardinal characteristics.\nIf the continuum hypothesis holds there is nothing in between, but otherwise these numbers can differ, and comparing them is a large part of modern set theory.\n",
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