This was a bonus question on an old assignment, unfortunately, I cannot find the solutions. The question asks to find an example of a finite dimensional vector space V over the rationals, where V is NOT a subset of the reals, and V is NOT a field. I'm not too sure how one would approach this problem, any help would be appreciated
2026-04-04 13:14:10.1775308450
Finite dimensional vector space V over the rationals which is not a subset of the reals and which is not a field
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What about $\mathbb{Q}^2$? It satisfies all of those conditions.