an infinite sequence,
x1,
x2, …, whose terms are points in
Ek, in
which there exists a point
y such that the limit as
n goes to infinity of
xn =
y if and only if for every ε>0, there exists a number
N such that
i>
N and
j>
N implies |
xi −
xj|< ε.
Also called Cauchy sequence, convergent sequence. Compare complete (def. 10b).