| 1 | \newpage |
| 2 | \section{Introduction} |
| 3 | |
| 4 | \subsection{Overview} |
| 5 | |
| 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 | |
| 10 | \subsection{Notation} |
| 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 | $x \leq y$. |