How can I write upside down real numbers symbol ($\mathbb{R}$)?
\umathbb{R}
for upside down\rmathbb{R}
for reflected\fmathbb{R}
for flipped
\documentclass{article}
\usepackage{amsfonts}
\usepackage{graphicx}
\makeatletter
\newcommand{\umathbb}[1]{{\mathpalette\dude@umathbb{#1}}}
\newcommand{\dude@umathbb}[2]{%
\raisebox{\depth}{\rotatebox{180}{$\m@th#1\mathbb{#2}$}}%
}
\newcommand{\rmathbb}[1]{{\mathpalette\dude@rmathbb{#1}}}
\newcommand{\dude@rmathbb}[2]{%
\scalebox{-1}[1]{$\m@th#1\mathbb{#2}$}%
}
\newcommand{\fmathbb}[1]{{\mathpalette\dude@fmathbb{#1}}}
\newcommand{\dude@fmathbb}[2]{%
\raisebox{\depth}{\scalebox{1}[-1]{$\m@th#1\mathbb{#2}$}}%
}
\makeatother
\begin{document}
$A\umathbb{R}B$ $A\rmathbb{R}B$ $A\fmathbb{R}B$
$X_{\umathbb{R}}$ $X_{\rmathbb{R}}$ $X_{\fmathbb{R}}$
\end{document}
To rotate upside down:
\documentclass{article}
\usepackage{amsfonts}
\usepackage{graphicx}
\begin{document}
X\rotatebox[origin=c]{180}{$\mathbb{R}$}X
\end{document}
Supports smaller math styles.
\documentclass{article}
\usepackage{amsfonts,scalerel,graphicx}
\newcommand\umathbb[1]{%
\ThisStyle{\rotatebox[origin=c]{180}{$\SavedStyle\mathbb{#1}$}}}
\newcommand\rmathbb[1]{%
\ThisStyle{\scalebox{-1}[1]{$\SavedStyle\mathbb{#1}$}}}
\newcommand\fmathbb[1]{%
\ThisStyle{\scalebox{-1}[1]{\rotatebox[origin=c]{180}{$\SavedStyle\mathbb{#1}$}}}}
\begin{document}
\[
A\mathbb{R}B\quad A\umathbb{R}B\quad A\rmathbb{R}B\quad A\fmathbb{R}B
\]
\[
X_{\mathbb{R}} X_{\umathbb{R}} X_{\rmathbb{R}} X_{\fmathbb{R}}
\]
\[
\mathbb{R}_{\mathbb{R}_{\mathbb{R}}}\quad
\umathbb{R}_{\umathbb{R}_{\umathbb{R}}}\quad
\rmathbb{R}_{\rmathbb{R}_{\rmathbb{R}}}\quad
\fmathbb{R}_{\fmathbb{R}_{\fmathbb{R}}}
\]
\end{document}