No matter what masses are chosen to stand in place of the electron, muon, and tau, the ratio Q is constrained to ⁠ 1 / 3 ⁠ ≤ Q < 1 . The upper bound follows from the fact that the square roots are necessarily positive, and the lower bound follows from the Cauchy–Bunyakovsky–Schwarz inequality. The experimentally determined value, ⁠ 2 / 3 ⁠, lies at the center of the mathematically allowed range. But note that removing the requirement of positive roots, it is possible to fit an extra tuple in the quark sector (the one with strange, charm and bottom).