{x}∈[0;1)
a)fie x∈Z, adica {x}=0
x+[x+1/2]=x+x=2x=[2x] adevarat
b) fie {x}∈(0;1/2)
[x} +[x]=2[x] ..dar si 2x =2[x]+2{x}<2[x]+1 deci [2x]=2[x]
c) fie {x}=1/2
[x]+[x+1]=2[x]+1..iar 2x= 2[x] +2*1/2=2[x]+1 adevarat
d)fie {x}∈(1/2, 1)⇒2{x}∈(1,2) si [2{x}]=1
[x]+[x+1}=2{x} +1 ..iar [2x]=[2[x]+2{x}}*=2[x]+[2{x}] =2[x]+1 addevarat
deci adevarat ∀x
* 2[x]∈Z desi iese din [....]
