The Irrational Numbers

GPTKB entity

Statements (23)
Predicate Object
gptkbp:instanceOf gptkb:mathematical_concept
gptkbp:cardinality uncountable
gptkbp:contains gptkb:The_Golden_Ratio
e
π
√2
√3
gptkbp:defines Numbers that cannot be expressed as a ratio of two integers
gptkbp:discoveredBy gptkb:Hippasus
gptkbp:hasSubgroup The Real Numbers
https://www.w3.org/2000/01/rdf-schema#label The Irrational Numbers
gptkbp:isDisjointWith The Rational Numbers
gptkbp:property dense in the real numbers
cannot be written as a fraction a/b, where a and b are integers and b ≠ 0
closed under addition with rational numbers (except for special cases)
every real number is either rational or irrational
non-repeating, non-terminating decimal expansion
not closed under addition or multiplication
product of two irrational numbers can be rational
sum of two irrational numbers can be rational
gptkbp:symbol ℝ \\ ℚ
gptkbp:bfsParent gptkb:Drew_Gress
gptkbp:bfsLayer 7