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.
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