%%% $$: empty formula or unmatched display?

When you try the following under \TeX's normal catcode
regime, you will get an error:

\beginverbatim
$$ $21-09$
\endverbatim

The message is:

\beginverbatim
! Display math should end with $$.
<to be read again>
                   2
l.7 $$ $2
         1-09$
\endverbatim

But how about this then:

\beginverbatim
\halign{#&#\cr $$ & $21-09$\cr}
\endverbatim

It magically works! The actual effect is similar to

\beginverbatim
\hbox{$$} (or) \hbox{${}$}
\endverbatim

In words of \TeXbook\ (chapter 25, page 287):

{\it%\beginverbatim
One consequence of these rules is that `\$\$' in restricted
horizontal mode simply yields an empty math formula.
}%\endverbatim

\endinput