The Modified Dirichlet Function

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This modified Dirichlet function has many names: Thomae, Riemann, popcorn, raindrop, ruler. It is defined on the closed interval to be at reduced rationals and elsewhere. It has the curious property that it is continuous on the irrationals but discontinuous at every rational in .


In contrast, the Dirichlet function (not shown here) is defined to be on the rationals and on the irrationals. It is discontinuous everywhere and its dull graph consists of two blurry lines.


Contributed by: George Beck (March 2011)
Open content licensed under CC BY-NC-SA



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