พูดคุย:Proof Hypercube 1

You say:

A more rigorous proof can also be achieved by considering other halfspaces and argue that it contains at least one of $h_{i}$.

Is the word contain ambiguous?? I can see all the points $x$ satisfying $x_{i}<0.5,\forall i$ lie below any other halfspace. But I think none of $h_{i}$ is completely contained in an other halfspace.