\title{Letters to the editor 2: Maths in \protect\LaTeX, Part 3}
\author{David Carlisle}
\begin{Article}

  The comments on the inadvisability of redefining user level commands
  are valid, but the example in question, \verb|\emptyset| in the AMS
  packages, is just due to an error in the first printing of \emph{The
    \LaTeX\ Companion} (as noted in \texttt{compan.err} in the \LaTeX\ 
  distribution.)  The `amssymb' package does not redefine
  \verb|\emptyset|. It still looks like a 0 with a line through it. The
  same glyph as in plain \TeX. \verb|\varnothing| is a slashed-circle.

Actually this raises an interesting side issue. The error in the
Companion printing was due to an error in the styles for \emph{Lucida}
fonts. (The Companion does not use the cm or AMS fonts). As Lucida
does provide both glyphs, it was simply an error to have the names
interchanged, but consider a hypothetical situation of a math font
family that only provides one slashed-closed-curve. How visually
dis-similar to $\emptyset$ may it be before it becomes unacceptable to
assign it to the command \verb|\emptyset|? For text fonts large differences
are acceptable. `Q' does not look much like `\texttt{Q}' but both are
accessed by `Q' and any differences are accepted by the reader as
differences in font design. In mathematics the situation is not at all
clear\ldots 

\end{Article}