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?
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2http://mathoverflow.net/questions/49551/dimension-of-infinite-product-of-vector-spaces – user26857 Apr 02 '15 at 12:40
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http://math.stackexchange.com/questions/1217128/the-dimension-of-vector-space-fx – user26857 Apr 02 '15 at 12:50