\(
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\newcommand{\catobj}[1] {\operatorname{Obj}(\mathrm{#1})}
\newcommand{\cathom}[1] {\operatorname{Hom}_{\cat{#1}}}
\newcommand{\multiBetaReduction}[0] {\twoheadrightarrow_{\beta}}
\newcommand{\betaReduction}[0] {\rightarrow_{\beta}}
\newcommand{\betaEq}[0] {=_{\beta}}
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\newcommand{\bm}[1] { \boldsymbol{#1} }
\require{physics}
\require{ams}
\require{mathtools}
\)
Math and science::Analysis::Tao::08. Infinite sets
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
[...].
A supporting lemma can be defined to design the proof:
In a conditionally (but not absolutely) convergent series, both the sum of
the positive terms and the sum of the negative
terms are [...].
