\(
\newcommand{\cat}[1] {\mathrm{#1}}
\newcommand{\catobj}[1] {\operatorname{Obj}(\mathrm{#1})}
\newcommand{\cathom}[1] {\operatorname{Hom}_{\cat{#1}}}
\newcommand{\multiBetaReduction}[0] {\twoheadrightarrow_{\beta}}
\newcommand{\betaReduction}[0] {\rightarrow_{\beta}}
\newcommand{\betaEq}[0] {=_{\beta}}
\newcommand{\string}[1] {\texttt{"}\mathtt{#1}\texttt{"}}
\newcommand{\symbolq}[1] {\texttt{`}\mathtt{#1}\texttt{'}}
\newcommand{\groupMul}[1] { \cdot_{\small{#1}}}
\newcommand{\inv}[1] {#1^{-1} }
\newcommand{\bm}[1] { \boldsymbol{#1} }
\require{physics}
\require{ams}
\)
Math and science::Analysis::Tao::06. Limits of sequences
Limits of sequences
If a sequence of reals \( (a_n)_{n=m}^{\infty} \) converges to a real \( L \), we say that \( (a_n)_{n=m}^{\infty} \) is
[...] and that \( L \) is the
[...]. We write:
\[ L = \lim_{n\to\infty}a_n \]
If a sequence does not converge to a real, then it is said to [...] or be [...]. \( \lim_{n\to\infty}a_n \) is left undefined for a divergent sequence.
