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Thomae's function

Thomae's function is a real-valued function of a real variable that can be defined as:: 531 f ( x ) = { 1 q if x = p q ( x is rational), with p ∈ Z and q ∈ N coprime 0 if x is irrational. {\displaystyle f(x)={\begin{cases}{\frac {1}{q}}&{\text{if }}x={\tfrac {p}{q}}\quad (x{\text{ is rational), with }}p\in \mathbb {Z} {\text{ and }}q\in \mathbb {N}…

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BoundedUnit intervalPeriodicIntegersDiscontinuous
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Thomae's function

Nodes46
Edges45
Triples33
Avg. degree1.96
Density0.043478
Components1

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Thomae's function

Top relations

related to Related probability distributions · 10
Thomae's function → Closed, DNA, Empirical, If, In, Li, The, Their, Thomae's, When
related to Properties · 9
Thomae's function → CCFFCC, Every, F0F2F5, If, Riemann, See, The, The Lebesgue, Thomae's
related to Related functions · 8
Thomae's function → Baire, Fσ, If, It, The, Therefore, This, Thomae's
see also · 3
Thomae's function → Blumberg, Euclid's, Thomae's
is a · 1
Thomae's function → real-valued function of a real variable that can be defined as

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Important terminology

function displaystyle rational numbers set thomae's real coprime number mathbb countable irrational discontinuities dirichlet integers dense would riemann integrable every

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Thomae's functionis areal-valued function of a real variable that can be defined as0.90text
the rational numbers - has measure zeroinstance ofEvery countable subset of the real numbers -0.80text
so the above discussion shows that Thomae's function is Riemann integrable on any intervalinstance ofEvery countable subset of the real numbers -0.80text
Thomae's functionrelated to PropertiesThomae's0.60section
Thomae's functionrelated to PropertiesF0F2F50.60section
Thomae's functionrelated to PropertiesCCFFCC0.60section
Thomae's functionrelated to PropertiesSee0.60section
Thomae's functionrelated to PropertiesRiemann0.60section
Thomae's functionrelated to PropertiesThe Lebesgue0.60section
Thomae's functionrelated to PropertiesEvery0.60section
Thomae's functionrelated to PropertiesThe0.60section
Thomae's functionrelated to PropertiesIf0.60section

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