[surreal-numbers] / notes / introduction.tex

\newpage
\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
$x \leq y$.
Commit	Line	Data
8484c2fd AT	1	\newpage
	2	\section{Introduction}
	3
420b0302 AT	4	\subsection{Overview}
420b0302 AT	5
cc0282e4 AT	6	These notes accompany the book Surreal Numbers by Donald Knuth, specifically
	7	the 1974 edition. They are only intended to further my own understanding; no
	8	guarantees of accuracy, relevance, or significance are extended.
	9
420b0302	10	\subsection{Notation}
cc0282e4 AT	11
	12	A surreal number $X$ consisting of left set $X_L$ and right set $X_R$ is
	13	represented as \surreal{X_L}{X_R}. The void set, as Knuth named it, is
	14	represented by leaving the appropriate left or right set empty, as in
	15	\surreal{}{}, the first surreal number defined.
	16
	17	When applying binary relations like less-than-or-equal to sets, the notation $X
	18	\leq Y$ means that, $\forall x \in X$ and $\forall y \in Y$, it holds true that
	19	$x \leq y$.