AI-created image
Statements (27)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:paradox
|
| gptkbp:appliesTo |
three or more dimensions
|
| gptkbp:category |
gptkb:logic
gptkb:mathematics gptkb:set_theory paradoxes |
| gptkbp:compatibleWith |
one dimension
two dimensions |
| gptkbp:dependsOn |
axiom of choice
|
| gptkbp:field |
gptkb:logic
gptkb:set_theory |
| https://www.w3.org/2000/01/rdf-schema#label |
Banach–Tarski paradox
|
| gptkbp:namedAfter |
gptkb:Alfred_Tarski
gptkb:Stefan_Banach |
| gptkbp:opposedBy |
intuitive notion of volume
|
| gptkbp:publicationYear |
1924
|
| gptkbp:publishedIn |
gptkb:Fundamenta_Mathematicae
|
| gptkbp:relatedConcept |
group theory
non-measurable set paradoxical decomposition |
| gptkbp:state |
A solid ball in 3‑dimensional space can be split into a finite number of pieces and reassembled into two identical copies of the original ball.
|
| gptkbp:uses |
infinite sets
rigid motions rotations and translations |
| gptkbp:bfsParent |
gptkb:Alfred_Tarski
gptkb:Stefan_Banach |
| gptkbp:bfsLayer |
4
|