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\section{Introduction}

\subsection{Overview}

These notes accompany the book Surreal Numbers by Donald Knuth, specifically
the 1974 edition. They are only intended to further my own understanding; no
guarantees of accuracy, relevance, or significance are extended.

\subsection{Notation}

A surreal number $x$ consisting of left set $X_L$ and right set $X_R$ is
represented as \surreal{X_L}{X_R}. The void set, as Knuth named it, is
represented by leaving the appropriate left or right set empty, as in
\surreal{}{}, the first surreal number defined.

When applying binary relations like less-than-or-equal to sets, the notation $X
\leq Y$ means that, $\forall x \in X$ and $\forall y \in Y$, it holds true that
$x \leq y$.
