Let ∑ k = 0 ∞ a k {\displaystyle {}\sum _{k=0}^{\infty }a_{k}} be a real series. A reordering of this series is a series ∑ k = 0 ∞ b k {\displaystyle {}\sum _{k=0}^{\infty }b_{k}} with b k = a σ ( k ) {\displaystyle {}b_{k}=a_{\sigma (k)}} for a bijective mapping σ : N → N {\displaystyle {}\sigma \colon \mathbb {N} \rightarrow \mathbb {N} } .
