This HTML5 document contains 27 embedded RDF statements represented using HTML+Microdata notation.

The embedded RDF content will be recognized by any processor of HTML5 Microdata.

Namespace Prefixes

Prefix	IRI
dct	http://purl.org/dc/terms/
dbo	http://dbpedia.org/ontology/
foaf	http://xmlns.com/foaf/0.1/
dbt	http://dbpedia.org/resource/Template:
rdfs	http://www.w3.org/2000/01/rdf-schema#
freebase	http://rdf.freebase.com/ns/
rdf	http://www.w3.org/1999/02/22-rdf-syntax-ns#
owl	http://www.w3.org/2002/07/owl#
n13	http://en.wikipedia.org/wiki/
dbp	http://dbpedia.org/property/
dbc	http://dbpedia.org/resource/Category:
prov	http://www.w3.org/ns/prov#
xsdh	http://www.w3.org/2001/XMLSchema#
gold	http://purl.org/linguistics/gold/
dbr	http://dbpedia.org/resource/

Statements

Subject Item

dbr:Schröder–Bernstein_theorem

rdfs:label

Schröder–Bernstein theorem

rdfs:comment

In set theory, the Schröder–Bernstein theorem states that, if there exist injective functions f : A → B and g : B → A between the sets A and B, then there exists a bijective function h : A → B. In terms of the cardinality of the two sets, this classically implies that if |A| ≤ |B| and |B| ≤ |A|, then |A| = |B|; that is, A and B are equipotent. This is a useful feature in the ordering of cardinal numbers.

owl:sameAs

freebase:m.015x7k

dbp:wikiPageUsesTemplate

dbt:Citation dbt:Nlab dbt:Cite_journal dbt:! dbt:Math dbt:Clear dbt:MathWorld dbt:Mr dbt:Citizendium dbt:Mathematical_logic dbt:Set_theory dbt:Logic dbt:Reflist dbt:Color

dct:subject

dbc:Cardinal_numbers dbc:Theorems_in_the_foundations_of_mathematics dbc:Articles_containing_proofs

gold:hypernym

dbr:Equipollent

prov:wasDerivedFrom

n13:Schröder–Bernstein_theorem?oldid=1065891311&ns=0

dbo:wikiPageID

44218028

dbo:wikiPageLength

17545

dbo:wikiPageRevisionID

1065891311

dbo:abstract

In set theory, the Schröder–Bernstein theorem states that, if there exist injective functions f : A → B and g : B → A between the sets A and B, then there exists a bijective function h : A → B. In terms of the cardinality of the two sets, this classically implies that if |A| ≤ |B| and |B| ≤ |A|, then |A| = |B|; that is, A and B are equipotent. This is a useful feature in the ordering of cardinal numbers. The theorem is named after Felix Bernstein and Ernst Schröder. It is also known as Cantor–Bernstein theorem, or Cantor–Schröder–Bernstein, after Georg Cantor who first published it without proof.

foaf:isPrimaryTopicOf

n13:Schröder–Bernstein_theorem