Convergence

Contents

Sequences

Let $V$ be a vector space over a field $F$ . Let $f$ be a function $f: V rightarrow F$ such that for all $a, b in F$ and $mathbf{x,y} in V$ ,

$f(amathbf{x} + bmathbf{y}) = af(mathbf{x}) + bf(mathbf{y})$ .

If $f$ is such a function as defined above, then $f$ is a linear functional on $V$ .