\(
\newcommand{\cat}[1] {\mathrm{#1}}
\newcommand{\catobj}[1] {\operatorname{Obj}(\mathrm{#1})}
\newcommand{\cathom}[1] {\operatorname{Hom}_{\cat{#1}}}
\newcommand{\multiBetaReduction}[0] {\twoheadrightarrow_{\beta}}
\newcommand{\betaReduction}[0] {\rightarrow_{\beta}}
\newcommand{\betaEq}[0] {=_{\beta}}
\newcommand{\string}[1] {\texttt{"}\mathtt{#1}\texttt{"}}
\newcommand{\symbolq}[1] {\texttt{`}\mathtt{#1}\texttt{'}}
\)
Math and science::Analysis::Tao::06. Limits of sequences
Bolzano-Weierstrass theorem
Let \( (a_n)_{n=0}^{\infty} \) be a bounded sequence (i.e. there exists a real
number \( M > 0 \) such that \( |a_k| \le M \text{ for all } k \in N \)). Then
there is at least one [...] which [...].
