Definition 12.2.3 (Unconditional Convergence).label Let $E$ be a normed vector space, then a series $\sum_{n = 1}^{\infty} x_{n}$ with $\seq{x_n}\subset E$ converges unconditionally if for any bijection $\sigma: \natp \to \natp$,
\[\sum_{n = 1}^{\infty} x_{n} = \sum_{n = 1}^{\infty} x_{\sigma(n)}\]