Let $F$ be a field and $I$ an arbitrary infinite index set. I'd like to know how to calculate the dimension of $\prod_{i\in I}F$.
By the way, I know $\dim(\prod_{i\in I}F)\geqslant 2^{\text{card}(I)}$. Does the equation always hold?
2026-04-03 00:00:27.1775174427
How to calculate the dimension of an infinite direct product of copies of a field?
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