Dirichlet function
Indicator function of rational numbers
In mathematics, the Dirichlet function is the indicator function 1 Q {\displaystyle \mathbf {1} _{\mathbb {Q} }} of the set of rational numbers Q {\displaystyle \mathbb {Q} } over the set of real numbers R {\displaystyle \mathbb {R} } , i.e. 1 Q ( x ) = 1 {\displaystyle \mathbf {1} _{\mathbb {Q} }(x)=1} for a real number x if x is a rational number and 1 Q ( x ) = 0 {\displaystyle \mathbf {1} _{\mathbb {Q} }(x)=0} if x is not a rational number (i.e. is an irrational number). 1 Q ( x ) = { 1 x ∈ Q 0 x ∉ Q {\displaystyle \mathbf {1} _{\mathbb {Q}...
Nº Q948386 ★★
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Dirichlet function
Indicator function of rational numbers
In mathematics, the Dirichlet function is the indicator function 1 Q {\displaystyle \mathbf {1} _{\mathbb {Q} }} of the set of rational numbers Q {\displaystyle \mathbb {Q} } over the set of real numbers R {\displaystyle \mathbb {R} } , i.e. 1 Q ( x ) = 1 {\displaystyle \mathbf {1} _{\mathbb {Q} }(x)=1} for a real number x if x is a rational number and 1 Q ( x ) = 0 {\displaystyle \mathbf {1} _{\mathbb {Q} }(x)=0} if x is not a rational number (i.e. is an irrational number). 1 Q ( x ) = { 1 x ∈ Q 0 x ∉ Q {\displaystyle \mathbf {1} _{\mathbb {Q}...
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From Wikipedia
In mathematics, the Dirichlet function is the indicator function 1 Q {\displaystyle \mathbf {1} _{\mathbb {Q} }} of the set of rational numbers Q {\displaystyle \mathbb {Q} } over the set of real numbers R {\displaystyle \mathbb {R} } , i.e. 1 Q ( x ) = 1 {\displaystyle \mathbf {1} _{\mathbb {Q} }(x)=1} for a real number x if x is a rational number and 1 Q ( x ) = 0 {\displaystyle \mathbf {1} _{\mathbb {Q} }(x)=0} if x is not a rational number (i.e. is an irrational number). 1 Q ( x ) = { 1 x ∈ Q 0 x ∉ Q {\displaystyle \mathbf {1} _{\mathbb {Q} }(x)={\begin{cases}1&x\in \mathbb {Q} \\0&x\notin \mathbb {Q} \end{cases}}} It is named after the mathematician Peter Gustav Lejeune Dirichlet. It is an example of a pathological function which provides counterexamples to many situations.
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