Prabhupada posted an Question
May 20, 2020 • 20:27 pm 30 points
  • IIT JAM
  • Mathematics (MA)

If a vectorspace is countable and field is also countable, then does it imply that the vectorspace is finitely generated vector space?

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  • Srinath best-answer

    Consider the vector space of real polynomials over the field of rational numbers. They are both countably infinte sets, but the basis of the vector space is not finite.

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    but your vectorspace is not countable , it is uncountable

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    In that case, the vector space should be set of all polynomials with rational coefficients.

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