**Definition** If the function $\sigma: \mathbb{N} \to \mathbb{N}$ is a [[Bijection|bijection]], then we call $\sum_{n=1}^{\infty} a_{\sigma (n)}$ a *rearrangement* of $\sum_{n=1}^{\infty} a_{n}$. ### Properties - [[Every rearrangement of a series with positive terms has the same limit]] so [[If a series is absolutely convergent then every rearrangement has the same limit]]. - [[Conditionally convergent series can be arranged to converge to any real number (Reimann Rearrangment Theorem)|Riemann Rearrangement Theorem]].