Every subset of a well-ordered set is well-ordered
,If A is a set, then a relation ≤ on A is a partial ordering if ... We say ≤ is a well ordering of A if every non-empty subset S of A has a least element. ,2021年6月15日 — Let X⊆T. By Subset Relation is Transitive, X⊆S. By the definition of a well ... ,Ramsey theory! Suppose A+B is not well-ordered. Then there is a strictly decreasing sequence a1+b1>a2+b2>⋯. Observe that for any i<j, ... ,Subsets of ordered sets. Define restrictions as in 3.3.f. Verify that if the relation ≼ on X has the following property, then its restriction to any set S ... ,is said to be well ordered (or have a well-founded order) iff every nonempty subset of A has a least element (Ciesielski 1997, p. 38; Moore 1982, p. ,由 P Howard 著作 · 1994 · 被引用 4 次 — DS: If a linear order has no infinite descending sequences then it is a well ordering. • LDF = F: Every linearly orderable Dedekind finite set is finite. ,Every element s of a well-ordered set, except a possible greatest element, has a unique successor (next element), namely the least element of the subset of all ... ,2017年1月8日 — Any subset of a well-ordered set is itself well-ordered. The Cartesian product of a finite number of well-ordered sets is well-ordered by the ... ,Well Orders. A well order (also referred as well-ordering or well-order relation) is a special type of total order where every non-empty subset has a least ...
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 Every subset of a well-ordered set is well-ordered 相關參考資料
3.7: The Well-Ordering Principle - Math LibreTexts
https://math.libretexts.org 5.3 Ordered Sets
If A is a set, then a relation ≤ on A is a partial ordering if ... We say ≤ is a well ordering of A if every non-empty subset S of A has a least element. https://www.whitman.edu Subset of Well-Ordered Set is Well-Ordered - ProofWiki
2021年6月15日 — Let X⊆T. By Subset Relation is Transitive, X⊆S. By the definition of a well ... https://proofwiki.org The sum of two well-ordered subsets is well-ordered
Ramsey theory! Suppose A+B is not well-ordered. Then there is a strictly decreasing sequence a1+b1>a2+b2>⋯. Observe that for any i<j, ... https://mathoverflow.net Well Ordered Set - an overview | ScienceDirect Topics
Subsets of ordered sets. Define restrictions as in 3.3.f. Verify that if the relation ≼ on X has the following property, then its restriction to any set S ... https://www.sciencedirect.com Well Ordered Set - Wolfram MathWorld
is said to be well ordered (or have a well-founded order) iff every nonempty subset of A has a least element (Ciesielski 1997, p. 38; Moore 1982, p. https://mathworld.wolfram.com Well Ordered Subsets of Linearly Ordered Sets - Project Euclid
由 P Howard 著作 · 1994 · 被引用 4 次 — DS: If a linear order has no infinite descending sequences then it is a well ordering. • LDF = F: Every linearly orderable Dedekind finite set is finite. https://projecteuclid.org Well-order - Wikipedia
Every element s of a well-ordered set, except a possible greatest element, has a unique successor (next element), namely the least element of the subset of all ... https://en.wikipedia.org Well-ordered set - Encyclopedia of Mathematics
2017年1月8日 — Any subset of a well-ordered set is itself well-ordered. The Cartesian product of a finite number of well-ordered sets is well-ordered by the ... https://encyclopediaofmath.org well-ordered set - Math24
Well Orders. A well order (also referred as well-ordering or well-order relation) is a special type of total order where every non-empty subset has a least ... https://www.math24.net |