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- $\forall T \subseteq S: \exists a \in T: \forall x \in T: a \preceq x$
This category has the following 2 subcategories, out of 2 total.
Pages in category "Well-Orderings"
The following 52 pages are in this category, out of 52 total.
- Set of Integers Bounded Below by Integer has Smallest Element
- Set of Integers can be Well-Ordered
- Set of Integers is not Well-Ordered by Usual Ordering
- Set of Non-Negative Real Numbers is not Well-Ordered by Usual Ordering
- Strict Well-Ordering Isomorphic to Unique Ordinal under Unique Mapping
- Strictly Increasing Mapping Between Wosets Implies Order Isomorphism
- Subset of Well-Ordered Set is Well-Ordered
- Well-Ordered Induction
- Well-Ordered Transitive Subset is Equal or Equal to Initial Segment
- Well-Ordering Minimal Elements are Unique
- Well-Ordering Principle
- Well-Ordering Theorem implies Hausdorff Maximal Principle
- Woset is Isomorphic to Set of its Initial Segments
- Wosets are Isomorphic to Each Other or Initial Segments
- Wosets are Isomorphic to Each Other or Initial Segments/Proof Using Choice
- Wosets are Isomorphic to Each Other or Initial Segments/Proof Without Using Choice