Hi Folks,

THis is my first exposure to Functional Analysis I am attempting to study and its proving a shock to my little brain. Here also is my first post which I hope is in the correct forum.

Let V be the vector space consisting of all infinite real sequences. Show that the subset W consisting of all such sequences with only finitely many non-0 entries is a subspace of V

If I write

$\displaystyle V^n={ (r_1, r_2, r_3) ; r_i \in R} $ for the vector V. Is this correct? Not sure how to represent the subset W.

$\displaystyle W^n={ (r_1, r_2, 0) ; r_{1,2} \in R} $?

Thanks