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並前往https://mathoverflow.net/questions/26/can-a-vector-space-over-an-infinite-field-be-a-finite-union-of-proper-subspaces

Can a vector space over an infinite field be a finite union of ...

You can prove by induction on n that: An affine space over an infinite field F is not the union of n proper affine subspaces. The inductive step goes like ...

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