Hi everybody, I've got an exercise about Banach spaces and I can't see how to solve it. It is a very simple problem and I know it might be some little detail I'm missing, and that is why I'm asking for help.

It says:

Let X be a Banach space with a monotone basis. Let $σ$ be the set of all finite block bases in the unit ball of X that contain at least one vector x

_{i}of norm 1. Suppose (y'_{1}, z'_{1}, y'_{2}, z'_{2},...,y'_{n}, z'_{n}) is in $σ$. Prove that the norms $\Vert \sum_{i=1}^n (y'_i + z'_i)\Vert$ and $\Vert \sum_{i=1}^n (y_i' - z'_i)\Vert $ are both at least 1/2.

Any help is welcome.

Thanks.