Given the metric space (ℝⁿ, d) with the usual metric d(x, y) = √Σ_{i=1}ⁿ(xᵢ - yᵢ) ², show that it is equivalent to the discrete metric.

a) Prove that d(x, y) ≤ 1 for all x, y in ℝⁿ.
b) Show that for any ε > 0, there exists N ∈ ℕ such that d(x, y) < ε for all x, y with N ≤ ε.
c) Demonstrate that the open balls generated by both metrics are the same.
d) Conclude that the usual metric is equivalent to the discrete metric.