Putting $$s in the middle of an `equation` environment: why doesn't Latex complain?

Question

I was surprised that the Latex code from a recent question didn't throw up any errors, and even more surprised on further investigation, that Crowley's explanation seems to be true. My intuition about the \begin{equation} ... \end{equation} code is clearly off, what's really going on?

Consider this, slightly adapted code:

\begin{equation} 
1: e^{i\pi}+1=0
$$  2: B\"ob $$ 
3: e=mc^2 
\end{equation}

This seems to prove that Crowley's explanation of such code, namely that "What that code says to LaTeX is begin equation, end it, begin it again, typeset definition of tangens and end the equation" is right: lines 1&3 can only be typeset in maths mode, line 2 only in text mode.

Shouldn't Latex see that the \end{equation} is ending a display math that wasn't started by the \begin{equation}?

Answer 1

Maybe it is because of environments math and displaymath.

I just tried those codes

\[\alpha$$ - works properly

\begin{displaymath}\alpha$$ - error (\begin{displaymath} ended by \end{document}) *

\displaymath\alpha$$ - works properly

\displaymath\alpha\displaymath - error (Bad math environment delimiter)

\displaymath\alpha\enddisplaymath - works properly.

Symetric options produce same results, so I think there's in LaTeX command definition

\newcommand{\[}{\displaymath}
\newcommand{\]}{\enddisplaymath }
\newenvironment{displaymath}{\displaymath}{enddisplaymath}

and in TeX something like

"if(displaymath)
 {$$ := \displaymath}
 else
 {$$ := \displaymath}"

Maybe I'm wrong, but this seems logical to me.

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• Note: That proves that I was wrong. Better words are It says: "Begin equation, switch to text mode, switch back to displaymath, typeset tangens definition and finally end the equation".