Plot[Sin[1/x],{x,-1/2,1/2},PlotStyle->{Black},Axes->Thick,Ticks->{{},{}}]

d[x_]:=Piecewise[{{1,Abs[Rationalize[x,0.01]-x]>0.004},{0,True}}];
DiscretePlot[d[x],{x,0,1,.005},PlotStyle->{Black},Ticks->{{},{}}]

maxq=100;
fracs=Table[p/q,{q,2,maxq},{p,2,q}]//Flatten//DeleteDuplicates;
pq={#,1/Denominator@#}&/@fracs;

ListPlot[pq,PlotRange->{0,.5},PlotStyle->{Black},AxesStyle->Directive[16,Thick,Black],Ticks->{{},{}}]