query: Subset of Well-ordered set A is Order-Isomorphic to A or section of A
positive_passages.docid: 27368
positive_passages.text: (Verification) $C \approxeq A$ or $C \approxeq \text{section of } A$ $\forall C$ s.t. $C \subset A$
negative_passages.docid: 85852
negative_passages.text: How many total order relations on a set $A$?
negative_passages.docid: 86748
negative_passages.text: Isomorphism of hom sets implies objects are isomorphic
negative_passages.docid: 22482
negative_passages.text: How can an ordered pair be expressed as a set?
negative_passages.docid: 54497
negative_passages.text: Set Notation - Inclusion and Proper Inclusion
negative_passages.docid: 117561
negative_passages.text: A set is infinite iff there is a one-to-one correspondent with one of its proper subsets?
negative_passages.docid: 82009
negative_passages.text: Prove that every totally ordered set has a well-ordered cofinal subset
negative_passages.docid: 144821
negative_passages.text: Number of ordered pairs of subsets
negative_passages.docid: 81843
negative_passages.text: Sequences of sets property
negative_passages.docid: 123613
negative_passages.text: Double Complement of a set proof
negative_passages.docid: 96025
negative_passages.text: Showing there is only one isomorphism between well ordered sets using transfinite induction
negative_passages.docid: 49143
negative_passages.text: Showing $A \subset B \iff A\cap B=A$
negative_passages.docid: 146062
negative_passages.text: A "Cantor-Schroder-Bernstein" theorem for partially-ordered-sets
negative_passages.docid: 77791
negative_passages.text: Proving an inclusion related to algebraic sets and interpreting it
negative_passages.docid: 147013
negative_passages.text: Subset of a finite set is finite
negative_passages.docid: 157218
negative_passages.text: If $E\subseteq X$ is connected, $E\cap A\neq\emptyset$ and $E\cap(X\setminus A)\neq\emptyset$ then $E\cap\partial A\neq\emptyset$
negative_passages.docid: 44974
negative_passages.text: Infinite set and countable subsets