Explicație pas cu pas:
{x}=x-[x]
a.{2x}=2x-[2x]=0
[2x]=2x ⇒x∈Z
b. {x}=1/3
x-[x]=1/3
[x]=x-1/3
[x]=(3x-1)/3=k , [x]≤x<[x]+1 , x=(3k+1)/3
k≤(3k+1)/3<k+1
3k+1≥3k⇒k∈Z
3k+1<3k+3⇒k∈Z
(3k+1)/3∈Z
3k+1∈M(3)⇒3k+1∈{0,3,6,9,,,3n} ,n∈N
⇒3k∈{-1,2,5,8,,,3n-1}⇒k∉Z⇒x∉R⇒x∈∅
