Statements (21)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:alsoKnownAs |
gptkb:Schröder–Bernstein_theorem
|
| gptkbp:appliesTo |
cardinality
infinite sets |
| gptkbp:category |
gptkb:logic
theorems in set theory |
| gptkbp:field |
gptkb:set_theory
|
| gptkbp:firstPublished |
late 19th century
|
| https://www.w3.org/2000/01/rdf-schema#label |
Cantor–Bernstein theorem
|
| gptkbp:implies |
If |A| ≤ |B| and |B| ≤ |A|, then |A| = |B|.
|
| gptkbp:namedAfter |
gptkb:Felix_Bernstein
gptkb:Georg_Cantor gptkb:Ernst_Schröder |
| gptkbp:relatedTo |
bijection
injection cardinal number |
| gptkbp:sentence |
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's_theorem_(set_theory)
gptkb:Bernstein–Cantor–Schroeder_theorem gptkb:Cantor's_theorem |
| gptkbp:bfsLayer |
5
|