Bernhard Riemann's rearrangement theorem

Let \( \sum_{n=0}^{\infty} a_n \) be a series of reals which is conditionally convergent, but not absolutely convergent, and let L be any real number. Then there exists a bijection \( j : \mathbb{N} \rightarrow \mathbb{N} \) such that [...].

In a conditionally (but not absolutely) convergent series, both the sum of the positive terms and the sum of the negative terms are [...].