Commit | Line | Data |
---|---|---|
8484c2fd AT |
1 | \newpage |
2 | \section{Introduction} | |
3 | ||
420b0302 AT |
4 | \subsection{Overview} |
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 | 11 | |
975cf9ad | 12 | A surreal number $x$ consisting of left set $X_L$ and right set $X_R$ is |
cc0282e4 AT |
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 | $x \leq y$. |