Symbols for ascending union/descending intersection

When writing on paper or on blackboard, I usually denote an ascending union by \bigcup with an upwards arrow at the end of the right prong. Likewise, I denote a descending intersection by \bigcap with a downwards arrow at the end of the right prong. Are these symbols included in any standard packages? If not, how can I define them?

MWE:

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

$\{0\}=\bigcap_n \left(-\frac1n,\frac1n\right)$
\end{document}

• I hope to remember well. IMHO the symbols with the arrows not exist. I think that they should be created. Aug 19 '20 at 11:51
• Unrelated but do not use the minimal class for MWEs: despite the name it is not suited. Use article instead. Aug 19 '20 at 12:02
• Aug 19 '20 at 13:09
• @campa: Still, wouldn't standalone be better than article? Or does it have similar problems? Aug 19 '20 at 14:11
• standalone loads article (unless you choose a different class with the appropriate option). Aug 19 '20 at 14:14

\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}


If you were always to be using it in \displaystyle, one could adapt to it:

\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}


• Very very nice....They are perfects. Aug 19 '20 at 12:23
• @tomasz It works for me...stackengine 2017/02/13 v4.01, using pdfTeX, Version 3.14159265-2.6-1.40.21 (MiKTeX 2.9.7300 64-bit). See ctan.org/pkg/stackengine for latest version. Aug 19 '20 at 13:34
• @StevenB.Segletes: I had a broken miktex installation. Fixing it now, should be okay. Still, I guess this is not going to work on arXiv for a while. :( Aug 19 '20 at 13:54

The symbols look much more like U-turns on a road sign, to be honest.

\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
\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
\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}


• Thanks! Small issue: in the displaystyle version, the alignment of $\infty$ and $n=1$ are a bit misaligned. Aug 19 '20 at 16:26
• @tomasz That's an optical effect due to the arrow. If you check the picture, you'll see that the infinity symbols are perfectly aligned with each other. To be honest, I'll restrain from using such symbols. Aug 19 '20 at 16:45
• My point is that I think it would look better with the symbols aligned with the cup/cap, not the whole symbol including the arrow. Aug 19 '20 at 16:54
• @tomasz I don't understand: the subscripts and superscripts are in the same exact position with or without the arrow. Aug 19 '20 at 17:22
• In the third line from the bottom, on the right, the middle of the $\infty$ sign is right above the top of the cap, and on the left, it is shifted towards the right. Aug 19 '20 at 17:24