Statements (60)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:cardinality |
gptkb:Continuum
|
| gptkbp:contrastsWith |
gptkb:Imaginary_Numbers
gptkb:Irrational_Numbers Integers Complex Numbers Rational Numbers |
| gptkbp:definedIn |
gptkb:Dedekind_cuts
Cauchy sequences |
| gptkbp:discoveredBy |
Ancient Greek mathematicians
|
| gptkbp:formedBy |
gptkb:Augustin-Louis_Cauchy
gptkb:Georg_Cantor gptkb:Karl_Weierstrass gptkb:Richard_Dedekind |
| gptkbp:hasAxiom |
Peano axioms (for natural numbers, extended to reals)
|
| gptkbp:hasSubgroup |
gptkb:Irrational_Numbers
Zero Integers Complex Numbers Rational Numbers Whole Numbers Algebraic Numbers Natural Numbers Negative Numbers Positive Numbers Transcendental Numbers |
| https://www.w3.org/2000/01/rdf-schema#label |
Real Numbers
|
| gptkbp:includes |
gptkb:Irrational_Numbers
Zero Integers Rational Numbers Whole Numbers Algebraic Numbers Natural Numbers Negative Numbers Positive Numbers Transcendental Numbers |
| gptkbp:notation |
R
ℝ |
| gptkbp:property |
Are closed under addition
Are closed under division (except by zero) Are closed under multiplication Are closed under subtraction Are uncountably infinite Are used to measure continuous quantities Can be positive, negative, or zero Can be represented as decimals Can be represented as infinite decimals Can be represented on the number line Form a complete ordered field Form a field Have the least upper bound property |
| gptkbp:symbol |
ℝ
|
| gptkbp:usedIn |
gptkb:Mathematics
gptkb:Physics Economics Engineering Statistics |
| gptkbp:bfsParent |
gptkb:Imaginary_Numbers
|
| gptkbp:bfsLayer |
6
|