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October 1st, 2009, 02:51 PM  #1 
Newbie Joined: Oct 2009 Posts: 1 Thanks: 0  Prove S is not finitely generated. please help
Let S={(a1,a2,a3,...)l ai c(belongs to) R, forall i c N} be the vector space of a infinite sequences of real numbers. (We know that S is a vector space over the feild R.) Prove carefully that S is not finitely generated. Can a spanning set equal all of the elements of S? Then the largest spanning set would be infinite because S has no limit to the elements in it. If I am wrong can someone please prove this or if I'm right and you would like to prove this as well, please be my guess. thank you 
October 1st, 2009, 03:59 PM  #2  
Senior Member Joined: May 2008 From: York, UK Posts: 1,300 Thanks: 0  Re: Prove S is not finitely generated. please help Quote:
Suppose there exists a finite basis Consider the vectors etc. The set is contained in and is linearly independent (easy to show). It is of dimension larger than the basis Can you see why cannot be a basis?  

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