Example of well ordered set
,In mathematics, a well-order on a set S is a total order on S with the property that every non-empty subset of S has a least element in this ordering. ,Example 1. · By definition, a partially ordered set is a well order if it is a total order and every non-empty subset has a least element. · The set 12,3,−4,−7 ... ,A remarkable property of the sequence of ordinal numbers is that each number corresponds to the well-ordered set of numbers that proceeds in the sequence: if we ... ,Example 5.3.2 Suppose S is a set and A is the set of all functions f:S→R. Let f≤g mean f(x)≤g(x) for all x∈S; ≤ is a partial ordering of A. Notice that ... ,well-ordered set ... Save This Word! noun Mathematics. a totally ordered set in which every nonempty subset has a smallest element with the property that there is ... ,2020年3月30日 — A set of real numbers is said to be well-ordered if every nonempty subset in it has a smallest element. · A well-ordered set must be nonempty and ...
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 Example of well ordered set 相關參考資料
Well-ordered set - Encyclopedia of Mathematics
https://encyclopediaofmath.org Well-order - Wikipedia
In mathematics, a well-order on a set S is a total order on S with the property that every non-empty subset of S has a least element in this ordering. https://en.wikipedia.org well-ordered set - Math24
Example 1. · By definition, a partially ordered set is a well order if it is a total order and every non-empty subset has a least element. · The set 12,3,−4,−7 ... https://www.math24.net Well Ordered Set - an overview | ScienceDirect Topics
A remarkable property of the sequence of ordinal numbers is that each number corresponds to the well-ordered set of numbers that proceeds in the sequence: if we ... https://www.sciencedirect.com 5.3 Ordered Sets
Example 5.3.2 Suppose S is a set and A is the set of all functions f:S→R. Let f≤g mean f(x)≤g(x) for all x∈S; ≤ is a partial ordering of A. Notice that ... https://www.whitman.edu Definition of Well-ordered set at Dictionary.com
well-ordered set ... Save This Word! noun Mathematics. a totally ordered set in which every nonempty subset has a smallest element with the property that there is ... https://www.dictionary.com 3.7: The Well-Ordering Principle - Mathematics LibreTexts
2020年3月30日 — A set of real numbers is said to be well-ordered if every nonempty subset in it has a smallest element. · A well-ordered set must be nonempty and ... https://math.libretexts.org |