Putting a union symbol inside union

Question

I would like to have a custom union symbol \ccup that is essentially two unions placed one inside another. A rotated \Subset works just fine for a "small" union, as shown in the image below; however, I need to have a similar symbol \bigccup for a "big" union just like \bigcup.

Rescaling \Subset does not look good at all for big unions. How could I make the symbol I need from scratch? Ideally, it should have the same dimensions as the original \bigcup.

Answer 1

Here an idea similar to Οὖτις's answer but trying to improve spacing. The trouble is that simply scaling \Cup does not work well, because the glyph sticks outside of its bounding box if compared to \bigcup:

\fboxrule.1pt \fboxsep-\fboxrule
\fbox{$\Cup$} \fbox{$\displaystyle\bigcup$}

For the scaling to work properly (and to obtain decently placed limits) we must first add some vertical padding.

\documentclass{article}

\usepackage{graphicx}
\usepackage{amsmath}
\usepackage{amssymb}

\makeatletter
\newcommand*{\bigCup}{\mathop{\mathpalette\big@Cup\relax}\slimits@}

\newcommand*{\big@Cup}[2]{%
   \setbox0=\hbox{\m@th$#1\Cup$}%
   \setbox0=\vtop{\vbox{\kern.2\ht0\copy0}\kern.1\ht0}%
   \setbox1=\hbox{\m@th$#1\bigcup$}%
   \vcenter{\hbox{\resizebox{!}{1.4\ht1}{\box0}}}%
}

\makeatother

\begin{document}

D: $\displaystyle\bigcup_a^b c \qquad \displaystyle\bigCup_a^b c$\par\medskip
T: $\bigcup_a^b c \qquad \bigCup_a^b c$\par\medskip
S: $\scriptstyle\bigcup_a^b c \qquad \bigCup_a^b c$\par\medskip
SS: $\scriptscriptstyle\bigcup_a^b c \qquad \bigCup_a^b c$

\end{document}

Short comments:

• One could try making the new symbol thinner but that starts deforming lines a wee bit too much for my taste.
• The \slimits@ comes from amsmath and is used by all sum-like big operators. It will obey the sumlimits/nosumlimits package options.

Answer 2

Based on this I propose the following as a starting point.

You can see that the linewidth of \bigCup is too much and it does not perfectly meet \bigcup's height, but right now I don't know how to fix that.

\documentclass{article}
\usepackage{amsmath,amssymb,scalerel}
\DeclareMathOperator*{\bigCup}{\scalerel*{\Cup}{\bigcup}}

\begin{document}
   This is inline: $A\Cup B$
   \begin{equation*}
      \bigCup_{i=1}^\infty A_i% your symbol
      \quad%
      \bigcup_{i=1}^\infty A_i% normal \bigcup
   \end{equation*}
\end{document}