Statements (19)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:alsoKnownAs |
gptkb:Cantor–Bernstein_theorem
gptkb:Cantor–Schroeder–Bernstein_theorem |
| gptkbp:appliesTo |
cardinality
infinite sets |
| gptkbp:category |
gptkb:mathematics
|
| gptkbp:field |
gptkb:set_theory
|
| gptkbp:firstPublished |
1898
|
| https://www.w3.org/2000/01/rdf-schema#label |
Schroeder–Bernstein theorem
|
| gptkbp:implies |
If |A| ≤ |B| and |B| ≤ |A|, then |A| = |B|.
|
| gptkbp:namedAfter |
gptkb:Felix_Bernstein
gptkb:Ernst_Schröder |
| gptkbp:relatedTo |
bijection
injection cardinal number |
| gptkbp:state |
If there exist injective functions from set A to set B and from set B to set A, then there exists a bijective function between A and B.
|
| gptkbp:bfsParent |
gptkb:Bernstein–Cantor–Schroeder_theorem
gptkb:Cardinal_Arithmetic |
| gptkbp:bfsLayer |
5
|