query: How to rigorously define ordered pairs?
positive_passages.docid: 22482
positive_passages.text: How can an ordered pair be expressed as a set?
negative_passages.docid: 120911
negative_passages.text: Clarification on proof: Order of left cosets equal
negative_passages.docid: 130975
negative_passages.text: Given a pair of continuous functions from a topological space to an ordered set, how to prove that this set is closed?
negative_passages.docid: 35714
negative_passages.text: Adjoint pairs, triplets and quadruplets
negative_passages.docid: 35972
negative_passages.text: Well ordering principle for rationals
negative_passages.docid: 7214
negative_passages.text: Does linear ordering need the Axiom of Choice?
negative_passages.docid: 91557
negative_passages.text: Show that total orders are maximal orders
negative_passages.docid: 33008
negative_passages.text: Linear order where every initial segment is finite
negative_passages.docid: 31113
negative_passages.text: Why is normal ordering a valid operation?
negative_passages.docid: 96025
negative_passages.text: Showing there is only one isomorphism between well ordered sets using transfinite induction
negative_passages.docid: 105686
negative_passages.text: Time-ordered operator in Srednicki
negative_passages.docid: 57724
negative_passages.text: How to prove boolean ordering question
negative_passages.docid: 3217
negative_passages.text: Construction of uncountably many non-isomorphic linear (total) orderings of natural numbers
negative_passages.docid: 150907
negative_passages.text: Notation and the name choice for meet and join (in order theory)
negative_passages.docid: 140106
negative_passages.text: How to prove a finite field is not ordered?
negative_passages.docid: 49157
negative_passages.text: First order theory - define a domain with an even number of elements
negative_passages.docid: 4103
negative_passages.text: Total ordering on complex numbers