EDB — 0W9

[0W9] Prerequisites:[0N1]↺↻.Sia \(𝜑(t)=t/(1+t)\). Let \((X_ i,d_ i)\) be metric spaces with \(i∈ℕ\), let \(X=∏_{i∈ℕ} X_ i\), for any \(f,g∈ X\) we define the distance on \(X\) as

Prove that \(d\) is a distance.