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April 25th, 2010, 12:48 PM   #1
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A infinite dimensional linear space

Let
Prove that is a linear space over with a basis
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April 25th, 2010, 01:23 PM   #2
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Re: A infinite dimensional linear space

What rules must S follow to be a linear space over Q?
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April 25th, 2010, 03:12 PM   #3
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Re: A infinite dimensional linear space

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April 26th, 2010, 08:05 AM   #4
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Re: A infinite dimensional linear space

Is that really all? (I thought there was more... but I may be wrong)

Anyway, does S satisfy this?

If so, what's left is to show that B is a basis. This should be immediate. THe definition of S gives us this directly.
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April 29th, 2010, 10:52 AM   #5
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Re: A infinite dimensional linear space

You have to prove that

That is, to prove B is linear independent over Q
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