Strong Convergence

Strong convergence is the type of convergence usually associated with convergence of a Sequence. More formally, a Sequence $\{x_n\}$ of Vectors in a normed space (and, in particular, in an Inner Product Space $E$ )is called convergent to a Vector $x$ in $E$ if

$$\Vert x_n-x\Vert\rightarrow 0\quad \hbox{as }n\rightarrow\infty.$$

See also Convergent Sequence, Inner Product Space, Weak Convergence