Simbol untuk serikat menaik / persimpangan menurun

Aug 19 2020

Saat menulis di atas kertas atau di papan tulis, saya biasanya menunjukkan penyatuan naik \bigcupdengan panah ke atas di ujung cabang kanan. Demikian juga, saya menunjukkan persimpangan menurun \bigcapdengan panah ke bawah di ujung cabang kanan. Apakah simbol-simbol ini disertakan dalam paket standar? Jika tidak, bagaimana saya bisa mendefinisikannya?

MWE:

\documentclass{article} 
\begin{document}
    \[
        (0,1)=\bigcup_n \left[\frac1n, 1-\frac1n\right]
    \]
    
    \[
        \{0\}=\bigcap_n \left(-\frac1n,\frac1n\right)
    \]
\end{document}

Jawaban

6 StevenB.Segletes Aug 19 2020 at 19:12
\documentclass{article}
\usepackage{stackengine,amsmath}
\stackMath
\DeclareMathOperator*\dcap{{\stackinset{r}{-1.02ex}{c}{-1.9pt}{\downarrow}
  {\bigcap}\mkern2mu}}
\DeclareMathOperator*\acup{{\stackinset{r}{-1.02ex}{c}{1.9pt}{\uparrow}
  {\bigcup}\mkern2mu}}
\begin{document}
    \[
        (0,1)=\acup_n \left[\frac1n, 1-\frac1n\right]
    \]
    
    \[
        \{0\}=\dcap_n \left(-\frac1n,\frac1n\right)
    \]
\end{document}

Jika Anda selalu menggunakannya \displaystyle, orang dapat menyesuaikannya:

\documentclass{article}
\usepackage{stackengine,amsmath}
\stackMath
\DeclareMathOperator*\dcap{{\stackinset{r}{-1ex}{c}{-3.1pt}{\downarrow}
  {\displaystyle\bigcap}\mkern2mu}}
\DeclareMathOperator*\acup{{\stackinset{r}{-1ex}{c}{3.1pt}{\uparrow}
  {\displaystyle\bigcup}\mkern2mu}}
\begin{document}
    \[
        (0,1)=\acup_n \left[\frac1n, 1-\frac1n\right]
    \]
    
    \[
        \{0\}=\dcap_n \left(-\frac1n,\frac1n\right)
    \]
\end{document}

3 egreg Aug 19 2020 at 22:58

Simbolnya lebih terlihat seperti putaran U di rambu jalan, jujur ​​saja.

\documentclass{article}
\usepackage{amsmath}

\makeatletter
\DeclareRobustCommand{\ubigcup}{\DOTSB\mathop{\,\ubigcup@\,}\slimits@}
\DeclareRobustCommand{\dbigcap}{\DOTSB\mathop{\,\dbigcap@\,}\slimits@}

\newcommand{\ubigcup@}{\mathpalette\ubigcup@@\relax}
\newcommand{\ubigcup@@}[2]{%
  \begingroup
  \sbox\z@{$\m@th#1\bigcup$}%
  \sbox\tw@{$\m@th#1\uparrow$}%
  \copy\z@
  \mkern-6.3mu\ifx#1\scriptscriptstyle\mkern0.3mu\fi
  \dimen@=\dimexpr\ht\z@-\ht\tw@
  \ifx#1\displaystyle\else
    \ifx#1\scriptscriptstyle\advance\dimen@ 0.5pt\else
      \advance\dimen@ 1pt
  \fi\fi
  \raisebox{\dimen@}[0pt][0pt]{\rlap{\copy\tw@}}%
  \mkern6.3mu\ifx#1\scriptscriptstyle\mkern-0.3mu\fi
  \endgroup
}
\newcommand{\dbigcap@}{\mathpalette\dbigcap@@\relax}
\newcommand{\dbigcap@@}[2]{%
  \begingroup
  \sbox\z@{$\m@th#1\bigcap$}%
  \sbox\tw@{$\m@th#1\downarrow$}%
  \copy\z@
  \mkern-6.3mu\ifx#1\scriptscriptstyle\mkern0.3mu\fi
  \dimen@=\dimexpr\dp\z@-\dp\tw@
  \ifx#1\displaystyle\else
    \ifx#1\scriptscriptstyle\advance\dimen@ 0.5pt\else
      \advance\dimen@ 1pt
  \fi\fi
  \raisebox{-\dimen@}[0pt][0pt]{\rlap{\copy\tw@}}%
  \mkern6.3mu\ifx#1\scriptscriptstyle\mkern-0.3mu\fi
  \endgroup
}

\makeatother

\begin{document}

$\displaystyle\ubigcup_{n=1}^{\infty} A_n$
$\displaystyle\bigcup_{n=1}^{\infty} A_n$

$\displaystyle\bigcup_{n=1}^{\infty} A_n$

\bigskip

$\textstyle\ubigcup_{n=1}^{\infty} A_n$
$\scriptstyle\ubigcup_{n=1}^{\infty} A_n$
$\scriptscriptstyle\ubigcup_{n=1}^{\infty} A_n$

\bigskip

$\displaystyle\dbigcap_{n=1}^{\infty} B_n$
$\displaystyle\bigcap_{n=1}^{\infty} B_n$

$\displaystyle\bigcap_{n=1}^{\infty} B_n$

\bigskip

$\textstyle\dbigcap_{n=1}^{\infty} B_n$
$\scriptstyle\dbigcap_{n=1}^{\infty} B_n$
$\scriptscriptstyle\dbigcap_{n=1}^{\infty} B_n$

\end{document}