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  "body": "\n## Definition\n\nLet $F$ be a field and let $V$ be a [[finite-dimensional|0ZHWKQMVX5]] vector space over $F$.\nThe *dimension* of $V$ over $F$, written $\\dim_F V$ or $\\dim V$, is the number of vectors in a [[basis|0KCQ9Y3QKA]] of $V$.\nFor an arbitrary vector space, the dimension is the cardinality of a basis.\n\n## Remarks\n\nThe number is well defined, by the [[dimension theorem for vector spaces|0WK0Y8RH1M]].\nThe zero space $\\{0\\}$ has the empty basis and dimension $0$.\nThe dimension depends on the field: $\\dim_\\C \\C = 1$, but $\\dim_\\R \\C = 2$.\nMathlib writes `Module.finrank F V` for the dimension as a natural number, with value $0$ for infinite-dimensional spaces.\n\n## Explanations\n\n### L1 human\n\nThe dimension counts the independent directions in a space.\nA line has dimension $1$, a plane has dimension $2$, and ordinary space has dimension $3$.\nEvery basis of a space has this same number of vectors.\n",
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