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Chapters: Zorn's Lemma, Well-Order, Total Order, Interval, Supremum, Ordered Pair, Dedekind Cut, Infimum, Ultrafilter, Monotonic Function, Directed Set, Möbius Inversion Formula, Cofinality, Upper and Lower Bounds, Embedding, Ascending Chain Condition, Incidence Algebra, Bounded Set, Hausdorff Maximal Principle, Preorder, Infinite Descending Chain, Partially Ordered Set, Galois Connection, Partially-Ordered Group, Causal Sets, Glossary of Order Theory, Completeness, Closure Operator, Stone Duality, Order Topology, Alexandrov Topology, Boolean Prime Ideal Theorem, Hasse Diagram, Dilworth's Theorem, Knaster-tarski Theorem, Lexicographical Order, Greedoid, Strict Weak Ordering, Comparability Graph, Infinite Divisibility, Complete Boolean Algebra, Well-Quasi-Ordering, Maximal Element, Graded Poset, Limit-Preserving Function, Specializationorder, Linear Continuum, Complete Heyting Algebra, Monomial Order, Complete Partial Order, Join and Meet, Residuated Mapping, Kruskal's Tree Theorem, Compact Element, Scott Domain, Distributivity, Fence, Supermodular Function, Completely Distributive Lattice, Majorization, Order-Embedding, Prewellordering, Antichain, Suslin's Problem, List of Order Theory Topics, Greatest Element, Order Dimension, Bourbaki-witt Theorem, Upper Set, Lubell-yamamoto-meshalkin Inequality, Covering Relation, Critical Pair, Linear Extension, Quantale, Bounded Complete Poset, Atom, Upper Topology, Schnyder's Theorem, Disjunction Property of Wallman, Countable Chain Condition, Trichotomy, Dickson's Lemma, Least Fixed Point, Order Isomorphism, Containment Order, Preordered Class, Scott Continuity, Bound Graph, Kleene-brouwer Order, Poset Topology, Kleene Fixed-Point Theorem, Pseudoideal, Frink Ideal, Weak Order of Permutations, Chain Complete, Ranked Poset, Dedekind Number, Countryman Line, Pasch's Theorem, Locally Finite Poset, Product Order, Interval Order, Fréchet Filter, Strong Antichain, Aronszajn Line, Dense Ord...More: http://booksllc.net/?id=10066673 ... Read more

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High Quality Content by WIKIPEDIA articles! In mathematics, the real numbers include both rational numbers, such as 42 and ?23/129, and irrational numbers, such as pi and the square root of two; or, a real number can be given by an infinite decimal representation, such as 2.4871773339..., where the digits continue in some way; or, the real numbers may be thought of as points on an infinitely long number line. These descriptions of the real numbers, while intuitively accessible, are not sufficiently rigorous for the purposes of pure mathematics. The discovery of a suitably rigorous definition of the real numbers?indeed, the realization that a better definition was needed?was one of the most important developments of 19th century mathematics. Popular definitions in use today include equivalence classes of Cauchy sequences of rational numbers; Dedekind cuts; a more sophisticated version of "decimal representation"; and an axiomatic definition of the real numbers as the unique complete Archimedean ordered field. These definitions are all described in detail below. ... Read more