Banach–Tarski paradox

GPTKB entity

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