In the text i am referring for Linear Algebra , following definition for Infinite dimensional vector space is given .
The Vector Space V(F) is said to be infinite dimensional vector space or infinitely generated if there exists an infinite subset S of V such that L(S) = V.
I am having following questions which the definition fails to answer :-
- Let us say i have an infinite dimensional vector space I(F) .If S is the infinite subset that spans I(F) , can i say that S is Linearly Independent . If so , why ?
- Does that mean any subset that spans every infinite dimensional vector space is Linearly Independent.
- On similar lines , can i say that Basis will exist for each Infinite Dimensional Vector Space and it is nothing but the subset that spans over vector space ?