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Exercise 1.6.18

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Let $e_{i}$ be the sequence with the only nonzero $i$ -th term $= 1$ . Then we have ${e_{i}}_{i \geq 0}$ is a basis. To prove it, we have that every sequence is linear combination of the basis since we only discuss the sequence with finite nonzero entries. Furthermore we have for every finite subset of ${e_{i}}_{i \geq 0}$ is linearly independent.

jephianlin

2011-06-27 00:00

Exercise 1.6.18

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