Statements (23)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
all sets
|
| gptkbp:category |
gptkb:logic
gptkb:set_theory |
| gptkbp:consequence |
there is an infinite hierarchy of infinities
|
| gptkbp:field |
gptkb:set_theory
|
| gptkbp:firstPublished |
1891
|
| gptkbp:hasCounterpart |
gptkb:Cantor–Bernstein_theorem
|
| gptkbp:hasProofMethod |
diagonalization
|
| https://www.w3.org/2000/01/rdf-schema#label |
Cantor's theorem
|
| gptkbp:implies |
the cardinality of the continuum is greater than that of the natural numbers
there is no surjective function from a set to its power set |
| gptkbp:language |
gptkb:German
|
| gptkbp:namedAfter |
gptkb:Georg_Cantor
|
| gptkbp:relatedTo |
gptkb:Cantor's_diagonal_argument
gptkb:continuum_hypothesis cardinality power set |
| gptkbp:sentence |
For any set A, the power set of A has strictly greater cardinality than A itself
|
| gptkbp:statedIn |
gptkb:Georg_Cantor's_1891_paper
|
| gptkbp:usedIn |
proof of the uncountability of the real numbers
|
| gptkbp:bfsParent |
gptkb:logic
|
| gptkbp:bfsLayer |
4
|