Convergent Sequence Space4 Discuss the set V of all convergent sequences as a vector space, where the addition of "vectors" and multiplication by a scalar are defined by
{an}+ {bn} = {an + bn} and c{an} = {can}.
Describe the zero element and additive inverse elements for this vector space. Make a conjecture about the dimension of V and try to back it up. Give at least one example of a non-trivial subspace and discuss its dimension?