 Restricting to a finite number of fermions at a time has the effect of splitting the Hilbert space of states into special subspaces called superselection sectors, which have the property that when \(\ket{\psi}\) and \(\ket{\phi}\) come from different sectors, any superposition \(a\ket{\psi} + b\ket{\phi}\) with \(|a|^2 + |b|^2 = 1\) will be a mixed state. It turns out in particular that the space describing the state in which all the fermions are \(z\)-spin-up is in a different superselection sector than the space in which they are all spin down. Although this may be puzzling for the newcomer, it can be found in any textbook that deals with superselection. And it allows us to construct an interesting supertask describing the measurement process. The following simplified version of it was given by Bell (1987).