Define a Cauchy sequence in a metric space (X, d).

A For every ε > 0, ∃N s.t. n ≥ N ⇒ d(x_n, x_1) < ε

B For every ε > 0, ∃N s.t. m, n ≥ N ⇒ d(x_m, x_n) < ε

C For every ε > 0, ∃N s.t. d(x_n, x) < ε for all n ≥ N