fund-amental sequence

an infinite sequence, x ₁ , x ₂ , …, whose terms are points in E_k, in which there exists a point y such that the limit as n goes to infinity of x_n = y if and only if for every ε>0, there exists a number N such that i > N and j > N implies | x_i − x_j |< ε. Also called Cauchy sequence, convergent sequence. Compare complete ( def 10b ).