Open ball in Discrete metric space

Question

I had encouterd in excercise that
Let $(X,d)$ be the discrete metric space then
Find 1.$B(x,1)$
2.$B(x,r),0<r\leq 1$
3.$B(x,r),r>1$
As per defination of discrete metric space
$d(x,y)=1$ for $x\neq y$
$d(x,y)=0$ for $x=y$
That means According to me $B(x,1)=x$ ,$2.B(x,r)=X$ and $3.B(x,r)=\phi$ But answer in the book is different
It says $B(x,r)=${x} for $0<r\leq 1$ and $B(x,r)=X$ for$r>1$ Where is my mistake lying .
ANy Help will be aprreciated