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Aug 20 at 17:07 comment added Chris Stuart Thanks, David. I have been trying to find the cardinality without assuming the continuum hypothesis.
Aug 20 at 0:36 history became hot network question
Aug 19 at 18:26 answer added Will Brian timeline score: 11
Aug 19 at 17:20 comment added David Gao Since $X$ satisfies the desired property iff $\text{span}(X)$ satisfies the desired property, the smallest cardinality of such $X$ and the smallest algebraic dimension of such $\text{span}(X)$ are the same. Clearly, this cardinality is at most $\mathfrak{c}$. It is also easy to see it is strictly larger than $\aleph_0$, so this solves the problem assuming CH, at least.
Aug 19 at 17:12 history edited David Gao CC BY-SA 4.0
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S Aug 19 at 16:35 review First questions
Aug 19 at 17:08
S Aug 19 at 16:35 history asked Chris Stuart CC BY-SA 4.0