How to redefine the "plus" symbol?

Question

Let's say I don't like the way the + symbol is printed inside equation: is there a way to change its appearance without defining a new command?

More generally, is it possible to create a command without the initial backslash?

Answer 1

Yes, of course.

\documentclass{article}
\begingroup
\catcode+=\active \gdef+{\mathbin{\mathrm{blurb}}} \endgroup \AtBeginDocument{\mathcode+="8000 }
\begin{document}
$x+y$
\end{document}

Of course you can think to better definition for the “math active” +. ;-)

---

A more general approach where you can also use an equivalent of the character being “redefined”.

\documentclass{article}
\makeatletter
\newcommand{\mathactivedef}[3][]{%
  \begingroup\lccode~=#2\lowercase{\endgroup\def~}{#3}%
  \if\relax\detokenize{#1}\relax
  \else
    @ifdefinable{#1}{\mathchardef#1=\mathcode#2\relax}% \fi \AtBeginDocument{\mathcode#2="8000 }%
}
@onlypreamble{\mathactivedef}
\makeatother
\mathactivedef[\keptplus]{+}{\mathbin{(\mkern-2mu\keptplus\mkern-2mu)}}
\begin{document}
$x+y$
\end{document}

In the optional argument to \mathactivedef you set the equivalent name that you can use in the body of the redefinition.

The previous “blurb” (without keeping the meaning of +) would be

\mathactivedef{+}{\mathbin{blurb}}

Answer 2

I found a really great, more general answer at https://newbedev.com/make-characters-active-via-macro-in-math-mode (at the bottom of the page).