Embedding Finite Metric Spaces into Normed Spaces

We recall that a metric space is a pair (X, ρ), where X is a set and ρ:X × X → [0, ∞) is a metric, satisfying the following axioms: ρ(x, y) = 0 if and only if x = y, ρ(x, y) = ρ(y, x), and ρ(x, y) + ρ(y, z) ≥ ρ(x, z).