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| | Surreal number - Wikipedia, the free encyclopedia |
 | | An obvious candidate would be finite induction, i.e., generate all numbers that can be constructed by applying the construction rule a finite number of times, but, as will be explained later on, things get really interesting if we also allow transfinite induction, i.e., apply the rule more often than that. |
 | | However, the relation ≤ defines only a total preorder, i.e., it is not antisymmetric. |
 | | The surreals have a total order: given any two surreals, they are either equal, or one is greater than the other. |
| en.wikipedia.org /wiki/Surreal_number (3289 words) |
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