Dedekind cuts

GPTKB entity

Statements (21)
Predicate Object
gptkbp:instanceOf gptkb:mathematical_concept
gptkbp:contrastsWith Cauchy completion
gptkbp:describes partition of rational numbers
gptkbp:field gptkb:mathematics
gptkb:set_theory
real analysis
gptkbp:hasApplication analysis
number theory
gptkbp:hasProperty every rational belongs to exactly one subset
lower set has no greatest element
each cut is a pair of non-empty subsets of rationals
https://www.w3.org/2000/01/rdf-schema#label Dedekind cuts
gptkbp:introducedIn 1872
gptkbp:namedAfter gptkb:Richard_Dedekind
gptkbp:relatedTo rational numbers
real numbers
Cauchy sequences
gptkbp:usedFor construction of real numbers
gptkbp:usedIn axiomatic construction of the reals
gptkbp:bfsParent gptkb:Surreal_Numbers
gptkbp:bfsLayer 5