P-Adic Numbers and P-Adic Analysis

Let X be a set and let ρ be a metric on X. Then ρ by definition has the following properties For all x, y ∈ X, ρ(x, y) ≥ 0 and ρ(x, y) = 0 if and only if x = y. For all x, y ∈ X, ρ(x, y) = ρ(y, x). For all x, y, z ∈ X, $$\rho \left( {x,z} \right)\rho \left( {x,y} \right) + \rho \left( {y,z} \right),$$ (the triangle inequality).