The vectorial relation between relative velocity and rapidity is β β = β β n = n tanh ⁡ ⁡ ζ ζ , and the "rapidity vector" can be defined as ζ ζ = ζ ζ n = n tanh − − 1 ⁡ ⁡ β β , each of which serves as a useful abbreviation in some contexts. The magnitude of ζ is the absolute value of the rapidity scalar confined to 0 ≤ ζ < ∞, which agrees with the range 0 ≤ β < 1.