65:. Cantor constructed a family of countable order types with the cardinality of the continuum, and in his 1901 inaugural dissertation Bernstein proved that such a family can have no higher cardinality.
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For the theorem that injections from A to B and from B to A imply a bijection between A and B, see
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88:. History of Mathematics. Vol. 25. American Mathematical Society. p. 3.
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There are equally many countable order types and real numbers
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780:Positive cone of a partially ordered group
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763:Positive cone of an ordered vector space
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42:of the second type class, the class of
7:
290:Properties & Types (
14:
746:Positive cone of an ordered field
600:Ordered topological vector space
1:
557:Series-parallel partial order
236:Cantor's isomorphism theorem
82:Plotkin, J. M., ed. (2005).
51:cardinality of the continuum
276:Szpilrajn extension theorem
251:Hausdorff maximal principle
226:Boolean prime ideal theorem
829:
622:Topological vector lattice
21:Schröder–Bernstein theorem
18:
144:
85:Hausdorff on Ordered Sets
231:Cantor–Bernstein theorem
36:Cantor–Bernstein theorem
775:Partially ordered group
595:Specialization preorder
57:and named by him after
261:Kruskal's tree theorem
256:Knaster–Tarski theorem
246:Dushnik–Miller theorem
753:Ordered vector space
591:Alexandrov topology
537:Lexicographic order
496:Well-quasi-ordering
572:Transitive closure
532:Converse/Transpose
241:Dilworth's theorem
800:
799:
758:Partially ordered
567:Symmetric closure
552:Reflexive closure
295:
53:. It was used by
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542:Linear extension
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271:Mirsky's theorem
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38:states that the
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792:Young's lattice
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365:Heyting algebra
313:Boolean algebra
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266:Laver's theorem
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180:Boolean algebra
175:Binary relation
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63:Felix Bernstein
55:Felix Hausdorff
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719:Order morphism
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637:Locally convex
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617:Order topology
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610:Order topology
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422:Chain-complete
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741:Ordered field
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697:Hasse diagram
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675:Comparability
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547:Product order
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520:Constructions
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417:Partial order
415:
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405:Join and meet
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303:Antisymmetric
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210:Weak ordering
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195:Partial order
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95:9780821890516
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49:, equals the
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813:Order theory
584:& Orders
562:Star product
491:Well-founded
444:Prefix order
400:Distributive
390:Complemented
360:Foundational
325:Completeness
281:Zorn's lemma
230:
185:Cyclic order
168:Key concepts
138:Order theory
84:
77:
59:Georg Cantor
35:
32:order theory
25:
768:Riesz space
729:Isomorphism
605:Normal cone
527:Composition
461:Semilattice
370:Homogeneous
355:Equivalence
205:Total order
47:order types
40:cardinality
736:Order type
670:Cofinality
511:Well-order
486:Transitive
375:Idempotent
308:Asymmetric
69:References
28:set theory
787:Upper set
724:Embedding
660:Antichain
481:Tolerance
471:Symmetric
466:Semiorder
412:Reflexive
330:Connected
44:countable
807:Category
582:Topology
449:Preorder
432:Eulerian
395:Complete
345:Directed
335:Covering
200:Preorder
159:Category
154:Glossary
687:Duality
665:Cofinal
653:Related
632:Fréchet
509:)
385:Bounded
380:Lattice
353:)
351:Partial
219:Results
190:Lattice
712:Subnet
692:Filter
642:Normed
627:Banach
593:&
500:Better
437:Strict
427:Graded
318:topics
149:Topics
92:
34:, the
702:Ideal
680:Graph
476:Total
454:Total
340:Dense
293:list
90:ISBN
61:and
30:and
707:Net
507:Pre
26:In
809::
505:(
502:)
498:(
349:(
296:)
130:e
123:t
116:v
100:.
98:.
23:.
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