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  "body": "\n## Definition\n\nLet $A$ and $B$ be [[sets|0SJ3RX9TXA]].\nThe cardinality of $A$ is at most the cardinality of $B$, written $|A| \\le |B|$, when there is an [[injective function|0PVG1CRAJN]] $f \\colon A \\to B$.\nWrite $|A| \u003c |B|$ when $|A| \\le |B|$ and $|A| \\neq |B|$.\n\n## Remarks\n\nThe relation does not depend on the choice of $A$ and $B$ in their classes of [[equinumerous|08EJHHMB5R]] sets.\nIt is reflexive and transitive. It is antisymmetric by the [[Schröder–Bernstein theorem|0A9V6RKQG6]].\nWith the axiom of choice, any two cardinals are comparable. See [[comparability of cardinals|0YBHSJMN3J]].\n\n## Explanations\n\n### L1 human\n\n$|A| \\le |B|$ means that $A$ fits into $B$ without two elements landing in the same place.\nFor example, $|\\mathbb{N}| \\le |\\mathbb{R}|$, because $\\mathbb{N}$ is a subset of $\\mathbb{R}$.\n",
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