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  "body": "\n## Summary\n\nThe transcendence degree of a [[field extension|0EQWVHF3W5]] $L/K$ is the cardinality of a [[transcendence basis|E45PA267S4]].\nIt counts the algebraically independent elements needed so that the rest is algebraic.\nIt does not depend on the choice of basis.\nIt is the field-theoretic notion of dimension: the function field of an irreducible variety has transcendence degree equal to the dimension of the variety.\n\n## Explanations\n\n### L1 human\n\nThe transcendence degree counts how many free variables a field extension has.\nThe field $\\C(x, y)$ has transcendence degree $2$ over $\\C$, like the plane.\nThe field of rational functions on a curve has transcendence degree $1$, like a line.\nAn extension has transcendence degree $0$ exactly when it is algebraic.\n",
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