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Exercise 2.A.15

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Proof. Let $m$ be a positive integer. Consider the list $v_{1}, \dots, v_{m}$ , where $v_{j}$ has $0$ in all slots except for a $1$ at the $j$ -th slot. This list is obviously linearly independent. Since $m$ was arbitrary, by the previous exercise $𝔽^{\infty}$ is infinite-dimensional. □

celiopassos

2017-10-06 00:00

Exercise 2.A.15

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