About: Cantor–Bernstein theorem

Facets (new session)
Description
Metadata
Settings
- Rule:
- Inverse Functional Properties:
- "Same As":

About: Cantor–Bernstein theorem Goto Sponge NotDistinct Permalink

An Entity of Type : owl:Thing, within Data Space : el.dbpedia.org associated with source document(s)

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.

Attributes	Values
rdfs:label	Schröder–Bernstein theorem (en)
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. (en)
sameAs	Cantor–Bernstein theorem
dbp:wikiPageUsesTemplate	dbt:! dbt:Citation dbt:Cite_journal dbt:Clear dbt:Color dbt:Math dbt:MathWorld dbt:Nlab dbt:Reflist dbt:Citizendium dbt:Mathematical_logic dbt:Mr dbt:Set_theory dbt:Logic
Subject	Articles containing proofs Cardinal numbers Theorems in the foundations of mathematics
gold:hypernym	Equipollent
prov:wasDerivedFrom	http://en.wikipedia.org/wiki/Schröder–Bernstein_theorem?oldid=1065891311&ns=0
Wikipage page ID	44218028 (xsd:integer)
page length (characters) of wiki page	17545 (xsd:nonNegativeInteger)
Wikipage revision ID	1065891311 (xsd:integer)
has 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. (en)
foaf:isPrimaryTopicOf	http://en.wikipedia.org/wiki/Schröder–Bernstein_theorem
is Wikipage redirect of	(Cantor-)Schröder-Bernstein theorem Bernstein-Schroeder theorem Cantor-Bernstein-Schroeder theorem Cantor-Schroder-Bernstein theorem Cantor–Bernstein–Schroder theorem Cantor–Bernstein–Schroeder theorem Cantor–Bernstein–Schröder theorem Schroder-Bernstein Theorem Schroder–Bernstein Theorem Schroder–Bernstein theorem Schröder-Bernstein Theorem Schröder–Bernstein Theorem Bernstein–Schroeder theorem (Cantor–)Schröder–Bernstein theorem Schroder-Bernstein theorem Schroeder-Bernstein theorem Schroeder–Bernstein theorem Schröder-Bernstein theorem Cantor-Bernstein-Schroder theorem Cantor-Bernstein-Schröder theorem Cantor-Berstein theorem Cantor-Schroeder-Bernstein theorem Cantor-Schroeder-Berntein theorem Cantor-Schroeder-Berstein theorem Cantor-Schröder-Bernstein theorem Cantor Schroeder Bernstein Theorem Cantor–Schroeder–Bernstein theorem Cantor–Schröder–Bernstein theorem Shroeder-Bernstein theorem Shroeder–Bernstein theorem
is Link from a Wikipage to another Wikipage of	List of theorems (Cantor-)Schröder-Bernstein theorem Axiom of choice Banach–Tarski paradox Bernstein's theorem Bernstein-Schroeder theorem Bijection Bijective proof Cantor's diagonal argument Cantor's theorem Cantor's theorem (disambiguation) Cantor-Bernstein-Schroeder theorem Cantor-Schroder-Bernstein theorem Cantor set Cantor–Bernstein–Schroder theorem Cantor–Bernstein–Schroeder theorem Cantor–Bernstein–Schröder theorem Cardinal number Cardinality Cardinality of the continuum Georg Cantor Myhill isomorphism theorem Cardinal assignment List of Banach spaces List of German inventions and discoveries List of examples of Stigler's law List of incomplete proofs List of mathematical logic topics List of mathematical proofs List of set theory topics Constructivism (philosophy of mathematics) Eilenberg–Mazur swindle Equinumerosity Ernst Schröder (mathematician) Implementation of mathematics in set theory Index of philosophy articles (R–Z) Bernstein–Schroeder theorem Felix Bernstein Group structure and the axiom of choice Injective function John Myhill (Cantor–)Schröder–Bernstein theorem Knaster–Tarski theorem

Faceted Search & Find service v1.17_git151 as of Feb 20 2025

Alternative Linked Data Documents: ODE Content Formats:

RDF

ODATA

Microdata

About

OpenLink Virtuoso version 07.20.3240 as of Nov 11 2024, on Linux (x86_64-ubuntu_focal-linux-gnu), Single-Server Edition (72 GB total memory, 927 MB memory in use)
Data on this page belongs to its respective rights holders.
Virtuoso Faceted Browser Copyright © 2009-2025 OpenLink Software