\(
\newcommand{\cat}[1] {\mathrm{#1}}
\newcommand{\catobj}[1] {\operatorname{Obj}(\mathrm{#1})}
\newcommand{\cathom}[1] {\operatorname{Hom}_{\cat{#1}}}
\newcommand{\multiBetaReduction}[0] {\twoheadrightarrow_{\beta}}
\newcommand{\betaReduction}[0] {\rightarrow_{\beta}}
\newcommand{\betaEq}[0] {=_{\beta}}
\newcommand{\string}[1] {\texttt{"}\mathtt{#1}\texttt{"}}
\newcommand{\symbolq}[1] {\texttt{`}\mathtt{#1}\texttt{'}}
\newcommand{\groupMul}[1] { \cdot_{\small{#1}}}
\newcommand{\groupAdd}[1] { +_{\small{#1}}}
\newcommand{\inv}[1] {#1^{-1} }
\newcommand{\bm}[1] { \boldsymbol{#1} }
\require{physics}
\require{ams}
\require{mathtools}
\)
Math and science::Analysis::Tao::06. Limits of sequences
Squeeze test
Let \( (a_n)_{n=m}^{\infty} \), \( (b_n)_{n=m}^{\infty} \) and \( (c_n)_{n=m}^{\infty} \) be sequences of real numbers such that:
\[ a_n \le b_n \le c_n \]
for all \( n \ge m \). Suppose that \( (a_n)_{n=m}^{\infty} \) and \( (c_n)_{n=m}^{\infty} \) both converge to the same limit \( L \). Then [...].
