An apparent paradox

You have infinite number of balls numbered 1,2,... at your disposal.At time(t)=0, you put balls numbered 1 to 10 into a box.At t=1/2, you put balls numbered 11 to 20 and remove ball-1 from it.Similarly at t=(1/2 + 1/4 ), you put balls numbered 21 to 30 into the box and remove ball-2 from the box.
t follows 1/2 +1/4 +1/8 +...
how many balls are present at t=1 ?

Surprisingly, number of balls in the box at t=1 is 0. For any ball numbered 'k' we can find t(=1/2 + 1/4 +...+ 1/2^k)when it is removed.
For a finite number of operations we can argue that 9 balls are added per each operation but this argument does not work when n->inf.In the language of limits,

Lt (x+9) - Lt (x) = 0
(x->inf) (x->inf)

and mind you LHS(not=)x+9-x=9