Initial commit of some notes related to chapter 1.

[surreal-numbers] / notes / introduction.tex

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 \newpage
 \section{Introduction}
 
 \newpage
 \section{Introduction}
 

-Hello, World!
+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.
+
+\section{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
+$x \leq y$.