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PlanetMath: well ordered set (208 words) |
 | A well-ordered set is a totally ordered set in which every nonempty subset has a least member. |
| An example of well-ordered set is the set of positive integers with the standard order relation |
| This is version 11 of well ordered set, born on 2001-10-17, modified 2005-07-26. |
| set theory: Information from Answers.com (1560 words) |
| Although musical set theory is often thought to involve the application of mathematical set theory to music, there are numerous differences between the methods and terminology of the two, and between typical mathematical terminology and the terms used in musical set theory more generally. |
| Musical set theory is therefore best regarded as a field that is unrelated to mathematical set theory, and is instead an application of combinatorics to music theory but with its own vocabulary, whose main connection to mathematical set theory is the use of the vocabulary of set theory to talk about finite sets. |
| For instance, in the cyclical ordering (0, 1, 2, 7), the interval between the first and second note is 1, the interval between the second and third note is 1, the interval between the third and fourth note is 5, and the interval between the fourth note and the first note is 5. |
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