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For questions related to teaching mathematics. For questions in Mathematics Education as a scientific discipline there is also the tag mathematics-education. Note you may also ask your question on http://matheducators.stackexchange.com/.

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Is it consistent with ZF that $V \to V^{\ast \ast}$ is always an isomorphism?

No, it’s not consistent. Let $V=k^{(\omega)}$ be the vector space of finite sequences of elements of $k$. Then $V^*$ can be identified with the vector space $k^\omega$ of all sequences, and elements …
Jeremy Rickard's user avatar