query: Discrete Mathematics ordered pairs and equivalence relations
positive_passages.docid: 29232
positive_passages.text: Find total number of relations that are equivalence as well as partial order set
negative_passages.docid: 66636
negative_passages.text: Problems with introducing ordered pairs axiomatically
negative_passages.docid: 118189
negative_passages.text: Proving the pairing axiom from the rest of ZF
negative_passages.docid: 5448
negative_passages.text: Finding the closure of some subsets of the ordered square
negative_passages.docid: 142840
negative_passages.text: Open axioms of equality
negative_passages.docid: 16687
negative_passages.text: Number of Equivalence relations of $\{1,2,3\}$
negative_passages.docid: 158009
negative_passages.text: Why is it always the case that, given an equivalence relation R on a set X and a $x \in X$, that x is equivalent to itself?
negative_passages.docid: 122506
negative_passages.text: Relation on countable sets
negative_passages.docid: 122839
negative_passages.text: how many different equivalence relations
negative_passages.docid: 52451
negative_passages.text: Ordered Triples and Set Theory
negative_passages.docid: 150857
negative_passages.text: Equivalence relations on S given no relation?
negative_passages.docid: 2396
negative_passages.text: Order-preserving injections of ordinals into $[0,1]$
negative_passages.docid: 120252
negative_passages.text: Equivalences of bounded sets definitions
negative_passages.docid: 3217
negative_passages.text: Construction of uncountably many non-isomorphic linear (total) orderings of natural numbers
negative_passages.docid: 96025
negative_passages.text: Showing there is only one isomorphism between well ordered sets using transfinite induction
negative_passages.docid: 48213
negative_passages.text: proving logical equivalence $(P \leftrightarrow Q) \equiv (P \wedge Q) \vee (\neg P \wedge \neg Q)$
negative_passages.docid: 1704
negative_passages.text: Define a relation and find its equivalence classes.