proof writing

[gusl]

Writing mathematical proofs is a difficult, interesting art, and I'd love to look at the kinds of miswrites, fixes, rewrites people make.

The camera-ready copy is due in about 19 hours.

Here's the most important page:


Any suggestions?

Is it easy to make LaTeX render squares instead of "QED"?

Comments

[mklip2001.livejournal.com]

Squares is easy... use "\Box" in math mode. Or, if you use the "proof" environment from the amsthm package, it will add a square automatically right-justified. If this is what you want to use, you should have
\usepackage{amsthm}
at the top, and then in your writeup you have
\begin{proof}
[Proof text here]
\end{proof}

[gustavolacerda.livejournal.com]

Thanks. I've been avoiding the "proof" environment because it puts the whole proof in italics.

[bhudson.livejournal.com]

The following may please you:

\def\EndProof{ \quad \vrule width 1ex height 1ex depth 0pt }
\newenvironment{proof}{\textbf{Proof}\hspace{4pt}}{\EndProof}

That is, unless you already have a proof environment, and then it may displease latex, and confuse you.

[gustavolacerda.livejournal.com]

Can I make my Theorem say "Corollary", or make the theorems skip a number?

[mklip2001.livejournal.com]

I don't know as much about skipping numbers. However, doing corollaries is not hard. So, I only described the "proof" environment. To create environments for theorems and whatever, after using the amsthm package, you want commands pretty high up like:
\newtheorem{corollary}{Corollary}

What this does is create a new environment, which is referred to by the first argument (i.e. corollary with lowercase c). To make a corollary, you'd then do
\begin{corollary}
This result is easy.
\end{corollary}

The second argument to newtheorem above tells LaTeX what to print in the document to represent this environment. So your thing would say "Corollary 1" in boldface, followed by "This result is easy." in italics.

Numbering is specific to each environment created this way. In other words, corollaries would maintain their own numbering scheme, I believe, separate from other theorems, i.e. each use of \newtheorem starts its own counter. I'm not sure how to change this. Using \newtheorem* instead turns off numbering.

[bhudson.livejournal.com]

To use the same counter as 'theorem', say:
\newtheorem{definition}[theorem]{Definition}

Special case:
\newtheorem{definition}{Definition}[section]
makes the third definition in section five be numbered 5.3

Apparently the optional argument can be anywhere. At least, empirically they can -- both those are drawn out of the same file.

[psifenix.livejournal.com]

Alternatively, you could just put $\square$ at the end of your proof.

[roseandsigil.livejournal.com]

In the amsmath proof environment, the correct way to change the QED is by redefining "qedsymbol", like

\renewcommand{\qedsymbol}{\square}

or maybe

\renewcommand{qedsymbol}{$\square$}

I don't know if this works in the non amsmath proof environment, but you could try.

[roseandsigil.livejournal.com]

er, that second one should be

\renewcommand{\qedsymbol}{$\square$}

[bhudson.livejournal.com]

I think the following can't possibly fail:

\renewcommand{\qedsymbol}{\mbox{$\square$}}