ianws

Toggling verbosity in LaTeX derivations (old)

2024-03-18T00:00:00+00:00

(An updated version of this post can be found here. This one is only kept for posterity.) \[\newcommand{\Fcal}{\mathcal{F}} \newcommand{\RR}{\mathbb{R}} \newcommand{\EE}{\mathbb{E}}\]

I find it helpful to write proofs so that they can optionally be made more verbose (e.g. to fill in certain details in a derivation). There’s a very simple trick you can use to accomplish this and it’s already built in to LaTeX — no additional packages needed. This idea was taken from this reddit comment.

Put the following in your preamble:

% Verbose LaTeX doc.
\newif\ifverbose % Define a new Boolean value "verbose".
% Initially it is false.
\verbosefalse % set verbose to true/false here.

Any content you would like to restrict to the “verbose” version of your paper should then be wrapped in \ifverbose <content> \if.

Demo

For the sake of example, consider the following short proof of the second Borel-Cantelli lemma (the proof details do not matter for the purposes of this post).

Claim: If $(E_k)_{k=1}^\infty$ are independent events and $\sum_{k=1}^\infty \Pr(E_k) = \infty$, then \[ \Pr \left ( \limsup_{n \to \infty} E_n \right ) = 1. \] Proof. Writing out the probability of $\limsup_{n} E_n$, we have $$\begin{align} &\quad \Pr \left ( \limsup_{n \to \infty} E_n \right )\\ &\equiv \Pr \left ( \bigcap_{m=1}^\infty \bigcup_{k = m}^\infty E_k \right ) \\ &{\color{lightgray}{= \lim_{m \to \infty}\Pr \left ( \bigcup_{k = m}^\infty E_k \right )}} \\ & \color{lightgray}{=1- \lim_{m \to \infty}\Pr \left ( \bigcap_{k = m}^\infty E_k^c \right ) }\\ & =1- \lim_{m \to \infty} \lim_{K \to \infty} \Pr \left ( \bigcap_{k = m}^K E_k^c \right ) \\ &= 1- \lim_{m \to \infty} \lim_{K \to \infty} \prod_{k=m}^K \left [1-\Pr \left ( E_k \right ) \right ]\\ &\geq 1- \lim_{m \to \infty} \lim_{K \to \infty} \exp \left \{ -\sum_{k=m}^K \Pr(E_k) \right \}\\ & \color{lightgray}{= 1- \lim_{m \to \infty} \exp \left \{ -\sum_{k=m}^\infty \Pr(E_k) \right \}}\\ & \color{lightgray}{= 1- \lim_{m \to \infty} 0}\\ &= 1, \end{align}$$ which completes the proof. $\square$

If the above derivations are written with the following TeX, then toggling between \verbosefalse and verbosetrue in your preamble will remove/include the lines in gray above, respectively.

\begin{align}
  \Pr \left ( \limsup_{n \to \infty} E_n \right )
  &\equiv \Pr \left ( \bigcap_{m=1}^\infty \bigcup_{k = m}^\infty E_k \right ) \\
  \ifverbose %BEGIN VERBOSE
  &= \lim_{m \to \infty}\Pr \left ( \bigcup_{k = m}^\infty E_k \right ) \\
  & =1- \lim_{m \to \infty}\Pr \left ( \bigcap_{k = m}^\infty E_k^c \right ) \\
  \fi %END VERBOSE
  & =1- \lim_{m \to \infty} \lim_{K \to \infty}  \Pr \left ( \bigcap_{k = m}^K E_k^c \right ) \\
  &= 1- \lim_{m \to \infty} \lim_{K \to \infty} \prod_{k=m}^K \left [1-\Pr \left ( E_k \right ) \right ]\\
  &\geq 1- \lim_{m \to \infty} \lim_{K \to \infty} \exp \left \{ -\sum_{k=m}^K \Pr(E_k) \right \}\\
  \ifverbose %BEGIN VERBOSE
  &= 1- \lim_{m \to \infty} \exp \left \{ -\sum_{k=m}^\infty \Pr(E_k) \right \}\\
  &= 1- \lim_{m \to \infty} 0\\
  \fi %END VERBOSE
  &= 1,
\end{align}

That’s all there is to it.

Bonus: if you use yasnippet in emacs or similar tools in neovim etc., it is very handy to have a snippet that creates the following.

\ifverbose %BEGIN VERBOSE
  %<content goes here>
\fi %END VERBOSE

Toggling verbosity in LaTeX derivations

2025-07-22T00:00:00+00:00

\[\newcommand{\Fcal}{\mathcal{F}} \newcommand{\RR}{\mathbb{R}} \newcommand{\EE}{\mathbb{E}}\]

I find it helpful to write proofs so that they can optionally be made more verbose (e.g. to fill in certain details in a derivation). There’s a very simple trick you can use to accomplish this and it’s already built in to LaTeX; — no additional packages needed. This idea is an adaptation of this reddit comment.

Put the following in your preamble:

% Verbose LaTeX doc.
\newif\ifverbose % Define a new Boolean value "verbose".
% Initially it is false.
\verbosetrue % set verbose to true/false here.

\newcommand{\verbose}[1]{\ifverbose\textcolor{gray}{\textit{verbose $\rightarrow$}}\quad #1\textcolor{gray}{\textit{non-verbose $\rightarrow$}}\quad \fi}

Any lines you would like to restrict to the “verbose” version of your paper should then be wrapped in \verbose{<content>}.

Demo

For the sake of example, consider the following short proof of the second Borel-Cantelli lemma (the proof details do not matter for the purposes of this post).

Claim: If $(E_k)_{k=1}^\infty$ are independent events and $\sum_{k=1}^\infty \Pr(E_k) = \infty$, then \[ \Pr \left ( \limsup_{n \to \infty} E_n \right ) = 1. \] Proof. Writing out the probability of $\limsup_{n} E_n$, we have $$\begin{align} &\quad \Pr \left ( \limsup_{n \to \infty} E_n \right )\\ &\equiv \Pr \left ( \bigcap_{m=1}^\infty \bigcup_{k = m}^\infty E_k \right ) \\ &{\ \color{lightgray}{= \lim_{m \to \infty}\Pr \left ( \bigcup_{k = m}^\infty E_k \right )}} \\ & \ \color{lightgray}{=1- \lim_{m \to \infty}\Pr \left ( \bigcap_{k = m}^\infty E_k^c \right ) }\\ & =1- \lim_{m \to \infty} \lim_{K \to \infty} \Pr \left ( \bigcap_{k = m}^K E_k^c \right ) \\ &= 1- \lim_{m \to \infty} \lim_{K \to \infty} \prod_{k=m}^K \left [1-\Pr \left ( E_k \right ) \right ]\\ &\geq 1- \lim_{m \to \infty} \lim_{K \to \infty} \exp \left \{ -\sum_{k=m}^K \Pr(E_k) \right \}\\ & \ \color{lightgray}{= 1- \lim_{m \to \infty} \exp \left \{ -\sum_{k=m}^\infty \Pr(E_k) \right \}}\\ &\ \color{lightgray}{= 1- 0}\\ &= 1, \end{align}$$ which completes the proof. $\square$

If the above derivations are written with the following TeX, then toggling between \verbosefalse and verbosetrue in your preamble will remove/include the lines in gray above, respectively.

\begin{align}
  \Pr \left ( \limsup_{n \to \infty} E_n \right )
  &\equiv \Pr \left ( \bigcap_{m=1}^\infty \bigcup_{k = m}^\infty E_k \right ) \\
  \verbose{ %BEGIN VERBOSE
  &= \lim_{m \to \infty}\Pr \left ( \bigcup_{k = m}^\infty E_k \right ) \\
  & =1- \lim_{m \to \infty}\Pr \left ( \bigcap_{k = m}^\infty E_k^c \right ) \\
  } %END VERBOSE
  & =1- \lim_{m \to \infty} \lim_{K \to \infty}  \Pr \left ( \bigcap_{k = m}^K E_k^c \right ) \\
  &= 1- \lim_{m \to \infty} \lim_{K \to \infty} \prod_{k=m}^K \left [1-\Pr \left ( E_k \right ) \right ]\\
  &\geq 1- \lim_{m \to \infty} \lim_{K \to \infty} \exp \left \{ -\sum_{k=m}^K \Pr(E_k) \right \}\\
  \verbose{ %BEGIN VERBOSE
  &= 1- \lim_{m \to \infty} \exp \left \{ -\sum_{k=m}^\infty \Pr(E_k) \right \}\\
  &= 1- 0\\
  } %END VERBOSE
  &= 1,
\end{align}

That’s all there is to it.

Bonus: if you use yasnippet in emacs or similar tools in neovim etc., it is very handy to have a snippet that creates the following.

\verbose{ %BEGIN VERBOSE
  %<content goes here>
} %END VERBOSE

(This is an updated version of an older post on the same topic)

A beamer theme inspired by macOS Keynote aesthetics

2025-07-28T00:00:00+00:00

A few years ago, I made a LaTeX beamer theme for presentations. In a nutshell, I began to adore the types of slides that could be made in Keynote on macOS but noticed three shortcomings:

Keynote does not run on Linux,
Its files are large relative to their content, and
Its math fonts don’t match the LaTeX ones.

Points 2 and 3 are minor annoyances but 1 is a deal-breaker for me. Fortunately, beamer is cross-platform, is very space-efficient, and math fonts are obviously native. However, I could not find a theme with the aesthetic sensibilities of Keynote so I attempted to make one and I have been using it ever since. Some screenshots of demo slides can be found below.

The rest of the demo slides can be found here.

Singapore

2025-12-08T00:00:00+00:00

Taipei, Taiwan

2025-12-08T00:00:00+00:00

Butte-aux-Cailles, Paris, France

2025-12-10T00:00:00+00:00

Seville, Spain

2025-12-10T00:00:00+00:00