Tutorial 0

Preamble

Exercise sheet

Overleaf

Go to https://www.overleaf.com/ (opens in a new tab) and make an account (if you don’t have one already).
Read through the tutorial here (opens in a new tab) .

Create project

Set up a new (blank) project in your Overleaf.
Give it a suitable project name, like “Assignments logical methods”.
Share that project with at least one of your fellow students.
Use main.tex to typeset the exercise below.
Create at least one more .tex file in the project and typeset it.

LaTeX gymnastics

Use the LaTeX cheat sheet for the book’s symbols.

Typeset the following in LaTeX. Use the tutorial and detexify (opens in a new tab) to look up unfamiliar commands. The fractions may be written with a horizontal fraction bar.

$0 \in ℕ$ , but $ω \notin ℕ$ (here $ω$ is the first infinite ordinal).
$ℕ = {0, 1, 2, \dots}$
$e iπ + 1 = 0$
$1/2 + 3/4 = 5/4$
$f : ℝ \to ℝ$ , $x \mapsto x + 2$
$1 \neq 0$
$(x i) i \in ℕ = (x₀, x₁, x₂, \dots)$
$□φ \to φ$
$f(x) = \sum i \in I f i (x) -1/2$
The LaTeX logo.
This is boldface, this is italic, this is sans, and this is code.

Solutions

These examples use \usepackage{amssymb} in the preamble. Several commands have alternatives; the examples below give one answer for each item.

$0 \in \mathbb{N}$, but $\omega \notin \mathbb{N}$.
$\mathbb{N} = \{0, 1, 2, \dots\}$
$e^{i\pi} + 1 = 0$
$\frac{1}{2} + \frac{3}{4} = \frac{5}{4}$
$f : \mathbb{R} \to \mathbb{R}$, $x \mapsto x + 2$
$1 \neq 0$
$(x_i)_{i \in \mathbb{N}} = (x_0, x_1, x_2, \dots)$
$\square\phi \to \phi$
$f(x) = \sum_{i \in I} f_i(x)^{-\frac{1}{2}}$
\LaTeX
This is \textbf{boldface}, this is \textit{italic}, this is \textsf{sans}, and this is \texttt{code}.

LaTeX speed challenge

How many symbols can you type in a minute? Start on easy and aim for ten correct answers. Once the commands feel familiar, try combining them on medium or tackling the longer expressions on hard.

Click the field to start, type the LaTeX for the symbol or expression shown, and press Enter. Don’t include dollar signs. For example, both \land and \wedge count for $\land$ . Spaces don’t affect your score. Shift+Enter skips a prompt; Escape ends the round.

Easy asks for individual symbols and subscripts. Medium combines symbols into expressions and adds text formatting. Hard also includes fractions, superscripts, and symbols such as $ℕ$ . Keep the cheat sheet handy for practice, then try a round without looking anything up.

Time: 1:00
Score: 0
Best: 0

Difficulty

Easy Medium Hard

One minute. Click the field, type the LaTeX for what the box shows, and press Enter. Shift+Enter skips a prompt, Esc ends the round.

Enable JavaScript to play. The LaTeX cheat sheet lists the same commands.