Let f(x)=sin(π/x)  and D+={x:f(x)>0}. Then D+  contains

D+={x:sin(π/x)>0}       ={x:πx∈∪n∈I(2nπ,(2n+1)π)}⊂{x:x∈∪n∈I(12n+1,12n)} This shows that D+⊃(1/3,1/2),D+⊃(1/5,1/4)  and D+⊃(−1,−1/2).