Thomae function

From specialfunctionswiki
(Redirected from Thomae)
Jump to: navigation, search

Thomae's function (sometimes called the popcorn function, raindrop function, Stars over Babylon) is given by the formula $$f(x) =\begin{cases} 1 & \text{if } x= 0 \\ \tfrac1{q} & \text{if } x = \tfrac{p}{q}\\ 0 & \text{if } x \in \mathbb{R}-\mathbb{Q}. \end{cases}$$


Properties[edit]

Thomae function is continuous at irrationals
Thomae function is discontinuous at rationals

Videos[edit]

Thomae Function by Bret Benesh (11 January 2012)
Thomae Function by Douglas Harder (19 April 2012)

See also[edit]

Modifications of Thomae's Function and Differentiability

References[edit]

[1]
[2]
[3]