A MathJax test

Here’s a test of my MathJax configuration.

Claim: you can’t have uncountably many nonintersecting T-shapes in \(\mathbb{R}^2\).

Proof: by contradiction. Consider the plane as a giant piece of squared paper, with the gridpoints being the points with integer coordinates. One of the squares contains uncountably many Ts.

In that square, let \(A_n\) be the set of all Ts with all branch lengths \(\geq 1/n\). One of these must be uncountable.

Finally observe that you can’t even have countably many Ts with bounded below branch length in a grid square. Consider the points where the horizontal and vertical branches of the Ts meet: it has to have a limit point.

MathJax allows you to use references to equations in the usual way. The following equation has \tag{1}\label{a} at the end

\[e^{i\pi} = -1 \tag{1} \label{a}\]

and (\ref{a}) without any dollar signs now produces (\ref{a}). MathJax can be configured to number equations automatically (i.e. without having to use tag) but it isn’t on by default.