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