# Weird formatting in a smaller created empty set symbol

A while back I created my own sort of emptyset symbol because the "not equal" slash didn't line up and it annoyed me. So I defined my own emptyset via \DeclareMathOperator{\vempty}{{\centernot{\Circle}}}. However, when I try to use it in a subscript (as demonstrated below), the slash becomes unaligned with the circle. Does anyone know how to remedy this? Here's my MWE:

\documentclass[12pt]{letter}
\usepackage{amsmath,amssymb,amsthm,centernot,cases}
\usepackage{wasysym}

\DeclareMathOperator{\vempty}{{\centernot{\Circle}}}
\DeclareMathOperator{\vempty}{{\text{\O}}}

\begin{document}
Example of difference between emptyset, varnothing, and vempty:
\begin{equation*}
\end{equation*}

Example of pathological behavior:
\begin{equation*}
\int_{\varnothing} f dm \quad \int_{\vempty} f dm
\end{equation*}
\end{document}


Symbols from wasysym are defined as

\mbox{\wasyfamily\symbol{<number>}}


so they don't change size in subscripts. Add \text around it.

Oh, and it's not an operator, but an ordinary symbol.

\documentclass[12pt]{letter}
\usepackage{amsmath,amssymb,amsthm,centernot,cases}
\usepackage{wasysym}

\newcommand{\vempty}{{\centernot{\text{\Circle}}}}

\begin{document}

Example of difference between emptyset, varnothing, and vempty:
\begin{equation*}

Personal note: I consider \varnothing a symbol good for plumbers. Your variation is even uglier. ;-)
• Is there a way to create a symbol which is more aesthetic and has the same slash angle as \neq? I tried, for example, \centernot{0}, but the slash was misaligned inside of the zero. – Isomorphism Jan 16 '19 at 0:04