- #1

jdc15

- 40

- 0

## Homework Statement

Since it's kind of hard to type out, I'll try to post a screenshot:

[PLAIN]http://img841.imageshack.us/img841/7357/questionq.jpg

## Homework Equations

There's the definition of a basis, vector space, and all the axioms.

## The Attempt at a Solution

I understand part A; it's simple enough, but I'm really stuck on part B. Had they been finite sets, as stated in our textbook E would be the standard basis for that finite set, i.e. {(1,0,0), (0,1,0), (0,0,1)} is the standard basis for R3. But somehow for infinite sequences this is not the case. Since I know by part A the set is linearly independent, it must be the second part of the definition of a basis that is violated, meaning it does NOT generate all infinite sequences. My initial guess is that sequences like {0,0,0,...0,0,1} can't be generated because j cannot reach infinity or something like that, but I don't know if it's correct to say that. Any ideas?

Thanks in advance.

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