\(
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\newcommand{\catobj}[1] {\operatorname{Obj}(\mathrm{#1})}
\newcommand{\cathom}[1] {\operatorname{Hom}_{\cat{#1}}}
\newcommand{\multiBetaReduction}[0] {\twoheadrightarrow_{\beta}}
\newcommand{\betaReduction}[0] {\rightarrow_{\beta}}
\newcommand{\betaEq}[0] {=_{\beta}}
\newcommand{\string}[1] {\texttt{"}\mathtt{#1}\texttt{"}}
\newcommand{\symbolq}[1] {\texttt{`}\mathtt{#1}\texttt{'}}
\)
Math and science::Analysis::Tao::06. Limits of sequences
Square root, expressed as the limit of a sequence
Let \( c \in \mathbb{R} \) be a real. The sequence defined recursively below
converges, and it converges to \( \sqrt{c} \).
Let \( x_1 = c \), and let \( x_n \) be defined like so:
[\[ x_{n + 1} = ?(x_n + \; ?) \]]
