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April 25th, 2010, 12:48 PM  #1 
Senior Member Joined: Dec 2006 Posts: 167 Thanks: 3  A infinite dimensional linear space
Let Prove that is a linear space over with a basis 
April 25th, 2010, 01:23 PM  #2 
Senior Member Joined: Oct 2007 From: Chicago Posts: 1,701 Thanks: 3  Re: A infinite dimensional linear space
What rules must S follow to be a linear space over Q?

April 25th, 2010, 03:12 PM  #3 
Senior Member Joined: Dec 2006 Posts: 167 Thanks: 3  Re: A infinite dimensional linear space 
April 26th, 2010, 08:05 AM  #4 
Senior Member Joined: Oct 2007 From: Chicago Posts: 1,701 Thanks: 3  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. 
April 29th, 2010, 10:52 AM  #5 
Senior Member Joined: Dec 2006 Posts: 167 Thanks: 3  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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dimensional, infinite, linear, space 
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